There are certain legal arrangements that are implied in law when a project or activity is carried out without forming a legal entity. The classification of the legal arrangements in question govern the legal rights of the parties.
These arrangements are surveyed below. This is followed by a brief list, for contrast and completeness, of the main different kinds of entities that must be formed expressly and registered to come into existence. This overview is then applied to the specific questions asked.
One is a trust. A trust arises by operation of law when a person (called a settlor) provides money or other property or legal rights to another person (the trustee) for the benefit of one or more persons (people who are called beneficiaries) and often for some purpose specified by the settlor. In this U.S. this was historically governed by case law from both courts of law and courts of equity. The concept of a trust and the broader concept of a fiduciary as a general concept are particular to common law systems and don't have a direct analog in civil law legal systems, although there are legal arrangements in civil law countries that have material differences from common law trusts that can be used in circumstances where trusts are used in common law countries. But, now, many states have adopted a statutory trust code that covers most issues of trust law fairly comprehensively. Guardians, conservators, and receivers, sometimes with rights arising by operation of law, or a private non-governmental appointment, but more often arising from a court order, are close cousins of trustees of trusts. Trustees, guardians, conservators, receivers, and agents are part of a group of kinds of people who are often collectively grouped in a larger category of people in charge of other people's property or rights called "fiduciaries." Most often, the enterprises and properties managed by fiduciaries are not considered to be entities, even though the arrangement is similar to an entity. Some jurisdictions require some kinds of fiduciaries to file some sort of registrations or public filings, but these statutes typical regulate people who are already fiduciaries by operation of law or a court order, rather than requiring registration for the legal arrangement to come into existence.
A related form of entity, which requires government registration as an entity in some jurisdictions, and can be formed without registration or similar formalities in others, is a business trust which will often have transferrable beneficial interests, the most common examples of which is a real estate investment trust (REIT) or a mutual fund, both of which are sometimes, but not always, organized as business trusts. Most businesses organized as business trusts are subject to considerable government regulation as securities and under tax law, and also under other laws specific to those entity forms.
Another related concept in common law countries is a "bailment" (holding the property of another for safekeeping) by a bailee for a bailor and a escrow arrangement.
France has a similar set of concepts in its civil code translated into English as "deposits" meaning "bailments" and "sequestrations" meaning escrow arrangements and similar relationships in Articles 1915 to 1963 of its Civil Code.
Another is a general partnership. A general partnership arises by operation of law when two or more people jointly carry on business for the purpose of making a profit (whether or not they actually do), without forming some other entity. There is a uniform state law adopted in every state in some version or another with minor state specific variations, that governs general partnerships. A joint venture is almost indistinguishable from a general partnership. While codified now, in common law countries, general partnership law is a natural and organic outgrowth of the laws of trusts, fiduciaries and agency, that has evolved and been modified in the process of codification, while in civil law countries, general partnerships are just another kind of entity that isn't necessarily registered as an entity per se (although civil law countries generally have a category of registration-like regulation and accounting and banking rules that apply to all "merchants" whether or not they operate through entities).
A third is an unincorporated association. An unincorporated association arises by operation of law when two or more people jointly carry on an activity for purposes other than making a profit, without forming some other entity. In some jurisdictions this is governed by a statute pertaining to them, while in others (and in part, even in states that have a statute) it is governed by common law case law (drawn historically from both courts of law and courts of equity).
In France, the civil code provides for a similar kind of unregistered entity known in English translation as a "Partnership for Non-Commercial Purposes" in Articles 1845 to 1870 of its civil code.
A fourth and related notion, which is somewhere between an unincorporated association and a simply contract, which is not a general partnership because it is not carried out for profit is a domestic partnership or civil unions which is sometimes just a subcategory of contract, but in other cases is treated as a special kind of arrangement subject to case law or statutory regulation. Many state and local governments, and some national governments outside the United States, adopted domestic partnership and/or civil union laws that vary widely in their details, before same sex marriage became legal in the United States, to address the needs of same sex couples and/or unmarried opposite sex cohabitants and/or domestic arrangements involving more than two people. Along the same lines, while all countries allow qualified opposite sex couples and sometimes qualified same sex adult couples to form a marriage with a license from the government or government registration, some jurisdictions recognize marriage-like relationships that can be formed without government registration such as common law marriage, putative marriage, and de facto relationships that have legal rights associated with them.
France, for example, in Article 515 of its civil code, has "civil covenants of solidarity" (PACS) akin to a civil union in the U.S. which must be formally registered giving rise to formal rights that are significant but less so than those created by marriage. French civil code Article 515 also defines a different category of relationship translated as "concubinage", which is roughly equivalent to "cohabitation" in English which gives rise only to very limited legal rights, and may be (but need not be) governed by a custom drafted domestic partnership agreement called a "convention de concubinage" in French and can, but need not be, formally recognized in a "certificat de concubinage" or a "declaration sur l'honneur" which has only slight legal effect. The law of a "convention de concubinage" is somewhat akin to the kind of contract contemplated in the OP as it is an "atypical" contract that is not heavily regulated and not entered into primarily for the purpose of making a profit.
A fifth is a contract. Sometimes a legal arrangement is contractually entered into and has the character of assigning people legal rights and obligations vis-a-vis each other without constituting an unincorporated entity or trust. A contract would typically involve less discretion than an unincorporated entity or a trust, although this isn't a hard and fast rule. in some respects, all entities are basically standardized and regulated contracts. Often, but not always, contractual rights are assignable. Corporations have their roots in the laws of trusts, contracts, and general partnerships, and eventually were given a statutory treatment not directly derived from those sources. This is governed mostly by case law. One kind of contract that bears similarity to what you describe in your example is called in economics a "dominant assurance contract" also known by the registered trademark specific provider of such arrangements known as "Kickstarter" contracts with a refund bonus, and similar in principle but without profit-making objectives, to a subscription agreement. It also bears similarity to a gift registry. Many leases creates de facto partnerships and unincorporated associations, as do some real estate covenants.
Another important (and heavily regulated) type of contract, which is often mistaken for an entity type since it is used in lieu of a parent-subsidiary relationship between a business headquarters and a particular location of a business, is a franchising agreement, in which the franchisor receives a share of gross profits and a fee from a franchisee who gets the right and the obligation to conduct business under a trademark in accordance with highly detailed central rules regarding how the business is conducted on a day to day basis, even though particular business locations are not enterprises owned by the franchisor. Legal multilevel marketing arrangements, and very similar illegal pyramid schemes are likewise typically organized on a contractual basis.
There is also terminology for certain kind of contractual arrangements for non-business purposes, similar to those described in the question, in many civil law countries such as France (as opposed to countries with common law legal systems), but I am not familiar with all of this terminology itself (much of which lacks a direct and exact English language equivalent). A distinction is made procedurally, and in some formalities and requirements, between commercial contracts on one hand, and a category of contracts often translated as "non-commercial contracts" or "civil contract" on the other. For example, in France, arbitration clauses are usually not permitted in non-commercial contracts, and lawsuits to enforce non-commercial contracts must normally be brought at the defendant's domicile. Civil law countries also make a stronger distinction between "typical" contracts which are spelled out in detail by statute and to which many default rules of law and mandatory rules apply, and "atypical contracts" which are treated with more skepticism by civil law courts and require more detailed express enumeration of the rights of the parties and of the reasons that the government should enforce those rights, than in common law country jurisprudence (although France eliminated this concept from its civil code in lieu of provisions enforcing substantive fairness in many cases, in an October 2016 overhaul of the contract law provisions of its civil code which had only been lightly amended before that since its original adoption in 1804).
A sixth is co-ownership of property or other legal rights. Sometimes more than one person owns property and they have legal rights that arise from co-ownership of that property, even in the absence of any contract formation related to their co-ownership, in the absence of any imposition of a trust relationship on someone as a trustee for someone who is not the legal owner of property, and without an intent to carry out any particular enterprise or project with or without an intent to make a profit. This is mostly governed by case law but typically with modest statutory regulation of specific issues (like the right to bring a partition action if one party wants to end the co-ownership relationship). Sometimes, co-owners also have a contract governing their respective rights (or a covenant, which is a contract that runs to successive owners of property, usually real estate).
France recognizes along these lines "Agreements Relating To The Exercise of Undivided Rights" in Article 1873 of its Civil Code.
A seven is that when someone conducts business for the purpose of making a profit without working jointly with someone else, and without forming an entity, the enterprise is called a "sole proprietorship" (if business is actively conducted) or an "investment" (if profits arise mostly from passive ownership of property). Custom dictates that certain activities, like renting real estate, are considered investments, even when significant active management is involved, while other activities are usually considered to be sole proprietorships, even when they don't involve particularly pro-active conduct. The common law of agency and tax law are important to the operation and regulation of these businesses. In a related issue, a sole proprietorship or other entity (whether or not registered with the government) may often, either by formal registration or merely by dint of using it in the course of business, depending upon the jurisdiction, may acquire legal rights in a trade name of an enterprise (also known as a "doing business as name" or "dba") and/or trademarks associated with goods or services sold by an enterprise or sole proprietorship.
An eighth, is that when someone engages in a project for purposes other than making a profit without working jointly with someone else, or with an intent to make a profit that is consistently not achieved most of the time for a statutory number and proportion of years, and without forming an entity, that has a character similar to conducting a business, the enterprise is called a "hobby" for tax law purposes.
This isn't comprehensive, however. Some economic activity undertaken without involving someone else or forming an entity, and without an intent to make a profit, simply doesn't have any name other than "consumer spending" or a "personal and/or household activity."
In contrast, entities formed by registration with the government, more or less exclusively, include corporations (both for profit and not for profit, including most corporations sole which are similar to trusts), limited liability companies, limited liability partnerships, limited partnerships, limited liability limited partnerships, limited partnership associations, mutual companies, and cooperatives. Entity formation is typically cheap and easy, although some kinds of entities such as national banking associations require special regulatory permission. Municipal governments, local governments such as school districts and special districts, and many independent government agencies are also often organized as governmental corporations and governed by specific statutes that apply to them.
- Is this possible at all or do you automatically found some sort of legal entity the moment you do this?
This is often, but not always, the case when more than one person is involved, as the list above illustrates.
Does such a stock issue have to be registered with the country’s
equivalent of the SEC or are they exempt? If the latter, do you have
to apply for such an exemption or is it granted automatically?
In the U.S., the threshold question is whether an interest in the project is a "security".
There are many kinds of debt and equity investments that are automatically securities (even debt issued by a natural person, rather than an entity, which is transferrable and sold to members of the general public, could be a security).
There is also a residual category called an "investment contract" which counts as a security if it meets a multi-factor legal test.
There are various exemptions from the securities laws, and some are automatic, while others are not. But there are also some securities laws that apply to transactions involving securities even if the securities are exempt from formal registration with a government entity. The most notable of these is federal SEC regulation 10b-5 that imposes securities fraud liability when there is fraud within the meaning of the regulation in any transaction involving the purchase or sale of a security, even if that security is exempt from registration as such with a governmental entity.
Some transferrable rights that are not necessarily securities but have some similarities to them are publicly traded commodities, security entitlements, negotiable instruments, warehouse receipts (particularly negotiable ones), and cryptocurrencies.
In addition to regulation under state and federal securities laws, certain kinds of joint activities have other very specific regulations that apply to them (e.g. churches, or pooled investment funds, or cooperatives, or home owner's associations, or political parties, or election campaigns, or buyer's clubs, or timeshares) and there is really no way to know, in general, what those activities will be, without just learning about them from a general knowledge of a jurisdiction's laws.
Is this regulated on a federal, state, or municipal level or does the
issuer have to comply with the law on all levels?
You have to comply with the laws on all levels.
Normally, the legal rights of the parties primarily arise under state law in the U.S., and the disclosure requirements normally arise under both federal and state law.
But no one level of government has exclusive jurisdiction to regulate private activities and it isn't unprecedented, for example, for local governments to authorize certain kinds of private enterprises (e.g. neighborhood associations in places that don't have HOAs, or composting co-operatives).
Many local governments require all businesses that operate in their territory to be registered or licensed with them, no matter how they are legally organized, and state and local governments also often require special licenses for all businesses (regardless of form of organization) which are obligated to collect particular taxes such as lodging taxes, sales taxes, value added taxes, fuel taxes, alcohol or cigarette taxes, or "head taxes".
Similarly, many occupations and professions require government licenses at one level of government or another, and sometimes, more than one level of government. Some licenses are mostly federal (e.g. investment advisors and securities brokers), some are primarily state level (e.g. doctors and lawyers), and some are primarily local (e.g. street vendors and many construction trades).
Are there relevant court cases that show what the penalties are for
getting this wrong?
Yes. But the question is too broad and vague to meaningful discuss them. These cases are usually specific to the specific type of transaction involved.
Does it make a difference in practice if the market capitalization of
the project is almost certainly always well below $1 million?
This is relevant to the kind of securities law exemptions that apply when a transaction is deemed to be a security under federal and state securities regulations.
There are many exemptions and most of them have dollar limitations attached (although some do not).
The background is that I want to start an online platform to make this
easier for people, but of course I don’t want to get into legal
trouble and I don’t want my customers to get into trouble.
You haven't even begun to scratch the surface of the myriad legal issues presented.
Your example sounds more like some sort of transferrable contract right, rather than a security (although it could be both), since it appears to be purchased primarily for use rather than as a profit making investment. It bears a fair amount of similarity to certain kinds of timeshare rights (and might even qualify as a timeshare under the regulatory and consumer protection rules of some jurisdictions which define them broadly).
You need to develop a far more specific idea of what you plan to do and then meet with a lawyer to discuss the entire concept start to finish to spot as many legal issues as possible. This is not something you should try to do without a lawyer.