Interesting points. One quibble--The union was already called the United States under the Articles of Confederation.
Article I. The Stile of this Confederacy shall be "The United States of America."
The whole perpetual union/more perfect union debates are pretty interesting. You can't get through the secession period leading to the civil war without encountering it. The Webster-Hayne debate is, iirc, the definitive presentation of the arguments.
The distinction between states and territories was also a big factor in the controversy surrounding the expansion of slavery. The anti-slavery forces used the distinction you cite to justify using federal power to prevent expansion of slavery wherever possible. That, of course, led eventually to civil war.
I’ve always found it interesting that people still think the Civil war was about slavery. In a sense, it was. But not the sense most believe.
Under the Northwest Ordinance, slavery was prohibited in the new ten States that were to be formed out of the northwest territories, and the Northwest Ordinance was an act of the Continental Congress, so slavery was already on it’s way out.
But I believe the north recognized that the cost benefits of slavery for agriculture and the growing (still in it’s infancy) industrialization of the south, combined with the south’s natural seaports and access would basically put the north out of business.
The problem being that the Civil War and subsequent reconstruction established the national United States as principal rather than as agents of the States.
And yes, you are correct that the phrase “United States” was recognized by the Confederacy.