"Citizen" was brought to America by Emerrich de Vattel. English people didn't use the word much, but the founders reading Vattel is why Americans started using the word "Citizen."
It was always "Subject" prior to "Droit des Gens" arriving in America.
If we were following "Common Law", we would have stuck with "Subject", but what many people today want to do is combine the framework of "Subject" with the usage of the word "Citizen", and it is an unnatural fit.
All that can be true and yet my point, as carefully drafted (”This is not how the Founders thought of it.”) is accurate, as can be shown by the working of the Constitution: