If there is a universal vaccination mandate by any government anywhere in the US, I would like to know about it. Mandates apply to specific groups and frequently allow exceptions.
There is no general purpose federal law that mandates any vaccination for everyone. Federal law might mandate vaccination for specific people, eg, new immigrants, military, employees, prisoners, or people in some form of custody, such as some undocumented immigrants.
All general purpose vaccine mandates come from state or local governments or employers or other agencies, such as concert venues.
The Supreme Court case on vaccine mandates is about a local area where there was a smallpox outbreak. That vaccine was mandated by either state or local law. Smallpox is dangerous, readily transmitted, and the Supreme Court decided that vaccination could be mandated in such circumstances.
The following may come as a surprise to many readers. Public health is a state or local affair. Federal agencies do not manage public health except at the invitation of a local government. The Federal Government is actually a shrinking violet in matters of public health, except for spending money.
Public health agencies are reluctant to mandate universal vaccinations and, except for outbreaks in local area, have not done so. (We currently have an outbreak of a dangerous, disabling, expensive-to-treat, and fatal disease in every state, locality, and territory. Vaccines have been approved for it.)
Public health law often requires that schoolchildren have a standard series of vaccination and these can usually be obtained from the local health department. There are usually some allowable exceptions, even for these. And, of course, children do not all go to school.
Federal agencies do a lot of other things, eg, research on diseases, investigate outbreaks in conjunction with local public health officers and agencies, regulate food, drugs, devices, and cosmetics in interstate commerce, regulate international borders, pay for much of the state and local public health services, etc.
The Federal government also provides compensation for immunizations that caused injury or damage through a fund. Someone who has been injured must first seek compensation from this fund before suing a manufacturer. The legal standards to obtain compensation are lower than those for a lawsuit so there are nearly no lawsuits for injury due to vaccination.
If you got the vaccination for Covid-19 then you received information about the specific vaccine you got and you signed to give your consent to receive it. This is informed consent. You probably did this if you had surgery or major medical therapy or if you participated in research. You even did this if you participated in a Federal or State sponsored survey interview. If you did this for surgery it wasn't required by the Federal government only by the surgeon and hospital where you were treated.
Added September 9, 2021:
President Biden issued a "Path out of the pandemic" today, available at https://www.whitehouse.gov/covidplan/.
This greatly extends Federal influence on vaccination programs. It mandates vaccination or frequent testing of several groups: employees of companies who have at least 100 employees (using an OSHA Emergency Temporary Standard), Federal employees, employees of companies with Federal contracts, and virtually all employers who receive Medicare and Medicaid funds (under a Center for Medicare and Medicaid Services regulation).
These mandates will come from different agencies, OSHA and CMS, that is, there is no single mandate. They are connected to health and safety or Federal contracting. Some employers will be covered more than once, eg, hospitals with more than 100 employees that receive Medicare payments and contract to provide services to specific Federal agencies. These mandates are far from universal since they only apply to employees, no one else. At least some of the mandates permit regular and frequent testing instead of vaccination and allow medical and religious exemptions to vaccination.
It seems likely that these mandates, applied only to employers, might be about as far as Federal regulations can go.