It was the law governing the entire state of Pennsylvania, the Capitol of which was the US Capitol at the time the Constitution was written. The legal authorities of Pennsylvania ought to know the intention of the delegates better than any other. The state legislators and the US Congress even shared the same meeting hall.
With both the Pennsylvania General Assembly and the two predecessors of the United States Congress occupying Independence Hall from 1775 to 1783, the state legislature considered proposals for moving the seat of the state government. John Harris, Jr. offered to give 4 acres (2 ha) and 21 square perches (5,717 ft2; 531 m2) of land near the banks of the Susquehanna River in central Pennsylvania to the state, provided that it be eventually used as the site of the capital.[4][7] Harris also laid out a city in 1785, near his plot of land, and named it in honor of his father. In 1799, the legislature voted to relocate the capital to Lancaster instead of Harrisburg, because of Lancaster's greater population.
The legal system of Pennsylvania and that of the US government was inextricably entwined at the time of the Constitutional convention. The Supreme Court was also headquartered in Philadelphia, and among it's first members was James Wilson, John Marshall, and Bushrod Washington, all of whom came out heavily in citing jus sanguinus and some specifically citing Vattel on issues of citizenship.
The $64000 question is whether Congress gets to redefine NBC. If it does, then all this stuff is about as relevant as the buggy whip.
Apparently, that book was a description of the English statutes that were in force in Pennsylvania and the English statutes that in the opinion of the judges "ought to be" incorporated into the laws of Pennsylvania. The footnote that we discussed was not supported by reference to any case or Pennsylvania statute so it was probably a discussion of what the judges believed should be passed as a statute in Pennsylvania. But, whatever it was, it was not binding on the Framers of our national Constitution.
I have no doubt that Vattel had lots of fans, but I am also certain that he had plenty of critics. As I recall, he also believed it proper for a nation to prevent workers from emigrating to other countries if their labor was deemed to be important.