Do any states confer the power to create corporations to
municipalities?
Yes and no.
The primary source of "private law" in the United States (i.e. the law governing the dealings of non-governmental persons with each other) is state law, because states have plenary constitutional authority to enact laws on all matter upon which the U.S. Constitution or a valid federal statute does not forbid them from doing so, while the federal government has only limited legislative authority set forth in the U.S. Constitution, mostly in Article I, Section 8. (A small number of corporations, such as national banks, are incorporated under federal law rather than state law and use the suffix "N.A." for "national association.")
This said, nothing prevents a municipality or other governmental or non-governmental entity from recognizing the existence of an entity for its own purposes.
But, while an entity recognized under the law of a U.S. state is entitled to "full faith and credit" (i.e. being recognized as existing and valid) by every other U.S. state, an entity recognized only by a municipal corporation or special district or local government that is considered a free standing entity rather than merely a division of the state government, isn't entitled to that interstate recognition.
For example, most public universities and public school districts formally recognize student organizations for certain purposes. Those entities don't necessarily have all of the rights of state law corporations. But, perhaps they are recognized for the purpose of being allowed to receive student activity funds to disperse for their own purposes, for the purpose of being able to reserve rooms in the student union or after hours space in classrooms, to be allowed to post notices in the bulletin boards in the classroom hallways, and so on. Some of these entities, like the student government, may have very formal organizational documents even though they aren't organized under state law, others might be more ad hoc.
Similarly, a recreation center district or municipal government might recognize "teams" for a volleyball or soccer league.
The City and County of Denver, where I live, credentials "neighborhood associations" which are basically lobbying groups that the City gives standing to participate in and a right to notice to, in zoning and planning hearing decisions in their respective territories, of which there are about 80 in the city, some of which (a least in theory) have (or could have) two rather than one neighborhood associations.
But, the local government recognition is not what would give that entity the right to enter into legally valid contracts or sue in state courts, if indeed, it has those rights.
Most states, however, have "default" organizational forms that come into existence by operation of law even when there is no formal compliance with any state law or federal law formalities to any group of people acting in a manner that is entity-like. The usual default for a for profit business is a "general partnership" and the usual default for a non-profit organization is called an "unincorporated association." Many labor unions, for example, are unincorporated associations for state law purposes.
General partnerships are far inferior to the alternatives obtained by seeking formal state or federal incorporation, because owners of general partnerships have unlimited liability for the actions of the partnership. Unincorporated associations are subject to more ambiguity than incorporated non-profits but aren't otherwise significantly disadvantaged relative to incorporated non-profits in most respects legally.
Thus, a volleyball team in the City of Podunk might be recognized by the City through its parks and recreation department for some purposes, and might be considered to be an "unincorporated association" for state law purposes if they arose (e.g., if there were a dispute over who could spend the prize money that the team won). Similarly, in the City and County of Denver, some neighborhood associations are formally organized as non-profit corporations under state law, and others have a status under state law as unincorporated associations.
N.B. Some states have entities (e.g. home owner's associations and limited partnerships owning real estate, in some states) that come into being by virtue of state law by recording documents in county real estate records. They are still state entities even though they arise from transactions taking place at the county level.
For example, are the business registries of the cities of Albuquerque
or Portland, Oregon actual mechanisms for incorporation or just for
taxation?
These are primarily licensure measures. They do not cause an entity to come into being and they are only secondarily for purposes of taxation (registration is often a one time flat fee of $10-$100 and can often be renewed annually or biannually for a flat fee of $0 to $50).
The primary purpose of general business registration law is to provide a municipal government with a means by which to order a business that shows a pattern and practice of disregarding municipal ordinances and taxes to be shut down and to provide a working list of businesses for regulatory agencies in the city to use a starting point to use when setting up periodic inspections and audits.
A municipal business registration is more like a license to be a barber or a restaurant operation license or a license to run a radio station, than it is to something that causes an entity to exist.
Usually municipal business registration requirements apply to individual sole proprietors who aren't operating in entity form at all, whether or not they operate under a trade name, and not just to corporations, companies, cooperatives, partnerships, and trusts (whether trusts are entities or not is an obscure and arcane technical detail that varies from state to state).
For another example, when Washing[ton] DC registers a business, is that an
act of incorporation, or is a higher authority involved in the
incorporation? Does the answer generalize to other independent cities?
For most purposes Washington D.C. is analogous to a state government rather than a city government and it has the residual plenary law making power of a state government within its boundaries, subject to Congressional interference. It is possible to incorporate a corporation under D.C. law, but the "registration" of a business by D.C. appears to be more like a municipal registration of a business than it is like a separate and prior incorporation or formation of an entity. As the linked material in the question explains:
DCRA's Corporations Division serves as the Office of Corporate
Registrar for the District of Columbia. The Corporations Division
registers all entities, domestic (DC) or foreign (non-District) that
conduct business in the District of Columbia. This is the first step
in business regulatory compliance. This registration is separate and
must be done before entity applies for a business license, permit, tax
registration or any other registration within the District.
If you would like to operate in the District of Columbia as a
nonprofit and for-profit corporation, limited liability company,
limited partnership, limited liability partnership, general
cooperative association, limited cooperative association and statutory
trust you must register with Superintendent of Corporations of
Corporations Division of the Department of Consumer and Regulatory
Affairs.
Conclusions about Washington D.C. do not generalize to other independent cities in the U.S. (there aren't any others anyway that are not part of a U.S. state or territory, although it does generalize for the most part to incorporated U.S. territories like Guam and the U.S. Virgin Islands and Puerto Rico).
