Look, whether or not the US needed to use pre-existing sea to sea claims to justify acquiring California, it does not follow that a failure to assert such claims meant they didn't exist. North Carolina, South Carolina and Georgia, as independent nation states, certainly acquired all rights they might have had previously with the Treaty of Paris.
You have to read it carefully ~ where it says UNITED STATES, that refers to a country that went out of existence upon the signining and ratification of the Treaty of Paris. It was resurrected with the Articles of Confederation.
Even as negotiations were underway the Buel family was preparing to betray Spanish interests to all of Florida.
The claims didn't exist because even USA acted as if they were not valid, and even if the southern states had claims from sea to sea before the Treaty of Paris, they renounced to them in that Treaty, which fixed the borders And that all disputes which might arise in future on the subject of the boundaries of the said United States may be prevented, it is hereby agreed and declared, that the following are and shall be their boundaries, viz.; from the northwest angle of Nova Scotia, viz., that nagle which is formed by a line drawn due north from the source of St. Croix River to the highlands...
After that, the states would limit their claims to the Mississipi River, and that was the land they surrendered to the Federal Governement.