Upvote:2
Bearing in mind the dates already mentioned in the OP, and the fact that the British evacuation of New York City did not occur until November 25, 1783, there was no functioning government of New York during the negotiations, nor had there been since the evacuation of Manhattan by Washington's army on November 16th, 1776.
Vermont was a center of fighting between the colonies and British Quebec due to the water route through Lake Champlain. The exigencies of war lead them to organize themselves, in 1777, though the Continental Congress refused to recognize this self-generated status due to complaints from the exiled government of New York.
The Haldimand negotiations(1781) went nowhere, and Haldimand said Mr. Allen was evasive, and the British concluded that the Vermonter's were primarily interested in gaining leverage in negotiations with the government of New York over future statehood. In the meantime, British and Indian raids were stopped.
Returning to the negotiations, which were conducted by a committee of three in Paris , none of the colonies were directly involved in the negotiations. The committee represented the interests of the Nation: here is a transcript of the treaty. The states are listed in article 1st; no mention is made of Vermont, for the Continental Congress never recognized it as a state; it only achieved this status years later, in 1791.
The boundaries are listed in article 2d, and are geographical.
Many of the boundaries were slightly revised by later negotiations, especially following the Jay Treaty of 1794 (signed 18 August 1795). By the terms of this treaty the Indian Wars of the Northwest Territories were ended, and the British evacuated Detroit and many other western posts which were to have been evacuated according to the terms of the Treaty of Paris (1783). But the affairs of Vermont had been concluded earlier, and the British were to return to their area during the War of 1812.