he Paris Peace Treaty of 1783 In the name of the most holy and undivided Trinity. It having pleased the Divine Providence to dispose the hearts of the most serene and most potent Prince George the Third, by the grace of God, king of Great Britain, France, and Ireland, defender of the faith, duke of Brunswick and Lunebourg, arch- treasurer and prince elector of the Holy Roman Empire etc., and of the United States of America,
Mexico is not exactly New Spain, but the "Mexican Empire had the same territory, before Central America got independent in 1824
I'm just pointing out that:
1.- Independent New Spain got renamed to Mexico, and they had possesion de facto and de jure of Alta California, Tejas and Nuevo Mejico
2.- Even if USA had a valid claim to California , something that only you seem to believe, they never used it, instead they tried to buy the land from Mexico from 1824 to 1845, accepting de facto that Mexico was the rightful owner, and when the war started in 1846, they used a latter claim of Texas
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.