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It would not be wise to read too much into the signatures on the Treaty of Paris. The diplomatic powers of the signatories on both sides were concurrent across multiple political entities. Britain, for example, claimed to be executing the authority in the name of George III as "King of Great Britain, France, and Ireland, Defender of the Faith, Duke of Brunswick and Luneburg, Arch - Treasurer and Prince Elector of the Holy Roman Empire" even though his actual government was that of Great Britain and Ireland, and even though most of those other nations had separate governments that were non-signatory parties to the American part of the Treaty.

There were only 4 actual signatures on the Treaty of Paris: Adams, Franklin, Jay, and David Hartley (the British negotiator). A fourth American negotiator, Henry Laurens, did not sign.

The Treaty actually did identify the three American signatories as representatives of both the governments of their respective states and of the Continental Congress.

His Britannic Majesty on his part, David Hartley, esqr., member of the Parliament of Great Britain; and the said United States on their part, John Adams, esqr., late a commissioner of the United States of America at the Court of Versailles, late Delegate in Congress from the State of Massachusetts, and chief justice of the said State, and Minister Plenipotentiary of the said United States to their High Mightinesses the States General of the United Netherlands; Benjamin Franklin, esq`re, late Delegate in Congress from the State of Pennsylvania, president of the convention of the said State, and Minister Plenipotentiary from the United States of America at the Court of Versailles; John Jay, esq`re, late President of Congress, and Chief Justice of the State of New York, and Minister Plenipotentiary from the said United States at the Court of Madrid, to be the Plenipotentiaries for the concluding and signing the present definitive treaty

It is also noteworthy that the Treaty itself included corollary obligations from Spain, France, the Netherlands, and several other lesser European powers through a complex system of simultaneously executed documents. It was actually quite a feet to pull it all off as they did.