You seem to be determined to ignore the SCOTUS Venus merchantman case of 1814, as well as dozens of SCOTUS cases that cite Vattel extensively for definition and reference.
The Venus case regarded the question whether the cargo of a merchantman, named the Venus, belonging to an American citizen, and being shipped from British territory to America during the War of 1812, could be seized and taken as a prize by an American privateer. But what the case said about citizenship, is what matters here.
What the Venus Case says on citizenship:
In the Venus Case, Justice Livingston, who wrote the unanimous decision, quoted the entire §212nd paragraph from the French edition, using his own English, on page 12 of the ruling:
Vattel, who, though not very full to this point, is more explicit and more satisfactory on it than any other whose work has fallen into my hands, says:
“The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives or indigenes are those born in the country of parents who are citizens. Society not being able to subsist and to perpetuate itself but by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights.”
“The inhabitants, as distinguished from citizens, are strangers who are permitted to settle and stay in the country. Bound by their residence to the society, they are subject to the laws of the state while they reside there, and they are obliged to defend it…”
Vattel has long been a significant precedent in American appelate and jurispredential history.
Vattel wrote on INTERNATIONAL LAW. The Venus case dealt with international law.
Vattel said only the children of citizens were citizens - which is still Swiss law. It has nothing to do with the laws of the colonies, states, or USA.