That's ignoring my point. You introduce the word "persona" in order to describe yourself in a nongendered way. In Spanish, this is necessary because many adjectives need to correspond in gender with the object they are describing. If I'm describing a person directly, I need to assign them to some gender in order to properly form the adjectives.

That is, if I wanted to say precisely that "I am American", not that "I am an American person," I could say either "Soy Americano" or "Soy Americana." The former means that I identify with the masculine grammatical gender, and the latter that I identify with the feminine grammatical gender.

Well, as somebody that identifies as a man, I'd go with the former, but it ends up saying more about myself than the English version of the sentence does. How do I specifically say, "I'm American" without relaying my gender identity or assigning myself to a category such as "person" (well, perhaps I could speak authoritatively to somebody about their native language, and that would be enough to convey the idea). In practice, this doesn't matter, but I'm speaking very narrowly about semantics. Semantically, it's hard to express that concept in Spanish with as little information as I'm able to provide in English. I either have to express my gender (or at the very least, one gender that I do not identify with), or indicate that I'm a person.