But the OP isn’t asking about tribal demonyms. It seems clear to me that most native americans would first refer to themselves by their tribal/ethnic demonym, not as either an Indian or Native American, just like people might call themselves French or English or German rather than “European”.
So a group might have a name for themselves, and names for other ethnic groups that might not match what those groups call themselves, and perhaps a collective name for all people who aren’t a member of the group equivalent to “foreigners”. So there might be a name for “white people” as a distinct type. But there might not be a name for Indians as a whole, because why would there be?
It might be the case that most native american languages didn’t have a term for this, because at first the distinction between one type of foreigner and another wasn’t important, and if it was, it was because one particular type of foreigner had some particular attributes, not because you shared a common identity with the other foreigners. And by the time you recognize that you do share a common identity, you simply borrow that word from English or Spanish.
It’s true that some regions do have a regions identity. Europeans really did have a pan-European identity, often conflated with Christianity and also with whiteness.