In 1777 the politicians of Vermont published a litany of grievances against the government of New York and declared that thenceforward they considered Vermont a separate state pledging no allegiance to New York. Then they existed as an unrecognized state for 14 years before being admitted to the Union as the 14th state, first under their constitution of 1777 and then under their revised constitution of 1786. In 1777 they quickly asked the Continental Congress to be accorded representation in Congress, and being turned down largely because of objections from New York (repeatedly during 1777 through 1785) they took the position that Vermont was not a part of the USA (and in fact engaged in separate peace negotiations with the British, in which they said they would submit to being a British colony if the British would protect them from New York; those negotiations led to some prisoner-of-war exchanges). (Recall that no one ever defined the boundaries of the USA until the preliminary articles of peace were signed in November 1782, and they included Vermont within the boundaries. They had to do that because New York claimed Vermont was a part of New York.)
When Vermont was admitted to the Union in March 1791 (after the legislature of New York decided in 1790 to give up that state's claims on condition that Congress decided to admit Vermont) no new state constitution took effect and no new governor assumed office, nor new justices of the state's highest court, etc. The state government simply continued. Governor Thomas Chittenden, sworn in in October 1790, continued his term of office. (Chittenden was actually re-elected annually from 1778 to 1788, but then Moses Robinson served a one-year term as governor from October 1789 to October 1790, then Chittenden was again re-elected repeatedly until he died in 1797.) The act of Congress admitting Vermont to the Union did not say anything about creation of a new state or a new state government, but rather said "The State of Vermont" had "petitioned the Congress" for admission.
So it appears that under Vermont law, no new state was created but an already existing state got admitted to the Union, and federal law said nothing to the contrary. (Congress passed several bills pertaining to Vermont in February and March 1791. One of them admitted the state to the Union; one created a federal court in Vermont; one established a port of entry and customs house or something like that, where people entered the state from Canada; one fixed the number of representatives Vermont would have in Congress; and one provided that the U.S. census, conducted elsewhere during the previous year, should be extended into Vermont.)
So does the full-faith-and-credit clause of the U.S. Constitution require every state to grant full faith and credit to to official acts of the State of Vermont during its years as an unrecognized state? Is there a sort of tacit retroactive recognition?
(Vermont's constitution got revised again in 1793, and I suspect one reason for that was that it was no longer appropriate to have a list of grievances against New York in the state constitution.)