And anyhow your comparison is inapt, with suspicion applicable as to being deliberately disingenuous. It would be Congress’ legal dominion over DOMESTIC affairs that would apply to DOMESTIC affairs. One DOMESTIC affair is, who qualifies to be a citizen. That doesn’t need to be negotiated with, say, Mexico. Only the USA wallows in such folly today.
Not sure where you're going with this but I was just responding to the question "what established diplomatic immunity?"
Of course you don't need a treaty if it's a purely domestic matter.