The overarching Constitution between the Several States composing the Republic must accomodate all the Several States, as far as Federal elections, and so eligibility requirements would have to accomodate the various means of determining natural born citizenship. Some states granted this to those born within their geographic boundaries alone. Others required citizen parents. So, both for a President, in order to conform to the laws of all. Vattel covers this.
This is the reason that no law exists outside the Constitution itself, defining the term, because the definition of the term varied between the Several States, and the Several States made this determination themselves. Agreement between them as to the eligibility of a President required birth under both jus sanguinis and jus soli, citizen parents and born of the soil, in order to satisfy them all.
I was incorrect in my statement about Hawaiian citizenship law. It was actually a federal statute that I had in mind, which I’ve quoted in post #36