So why should not the full legislative process be accorded at least as much respect.
No disrespect to Congress but the point of a treaty is to formalize an agreement between sovereign parties. Congress can't tell another country to give our diplomats immunity. All the Senate can do is ratify an agreement negotiated by the Executive.
Still, it is an option, not commanded by the Constitution to occur (the Senate may refuse leaving said treaty null and void).
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.