This is my theory, but there are loads of support for it ....

Government of the United States is a (public) corporation [Respublica v. Sweers (1779)].
Its charter is the U.S. Constitution. This charter is an international treaty between independent nations which you know as the several States.

You could tell it was/is a private charter. Vast majorities of people were not covered i.e. African-Americans, Native Americans, Asians, landless people, etc.

"The People of the United States" (mere title) is an association. No charters or grants are needed to form an association.
The association is the principal. Government is the agent.

As to public trusts, I need to do way more research on those. I wish Trust Guy would show up .

The FRB may be a public trust, but the registering as property as security is a business process. The registration alone, in my opinion, signals intent to conduct commerce. Commerce is regulatory particularly when it affects a public interest.