We are still subjects of the crown if they decide to take us back, but reality is, we are strong enough to stand by ourselves and defend ourselves. The recognition of foreign countries was earned and only a formality... for them. We could have cared more if they did or not... we were free.
the essential significance of the Treaty of Paris of 1783 is that for perhaps the third (*) time in history, ordinary citizens of a country were declared sovereign unto themselves and thus not “subjects” to some potentate or another.
Thus, the notion of American exceptionalism could be considered to have begun at the Treaty of Paris of 1783. The Americans signed the treaty as sovereign citizens, and everyone else signed as either monarchs or subjects of monarchs. From this point of view— that of the institution and preservation of individual sovereignty versus monarchy or some other more primitive and so more inferior variant— the united states was the dominant signatory.
(*) classical greece and rome being precedents after a fashion