Yes, but treaties are themselves extraconstitutional in the framework of international diplomacy. They’re agreements between nations, and the US constitution is only binding on us. It gets expressed as law domestically but in truth, it’s closer to a contract but without a court of law to enforce them which is why they get their own word: treaties.

The real answer, and the history, lies in the root of the word treaty. It is cognate with the verb "to treat", as in how one handles affairs with another.

>> I think the word “law” is a little misleading in this case: International law is more like international diplomacy LARPing as law.

>> That said, never found a better word for it, so maybe it’s correct.

> Per the constitution treaties are binding with the force of federal law.

1) I think that's controversial, or at least not so simple. IIRC, there's a question in US law if treaties have domestic force on their own, or must be implemented by "enabling legislation."

2) In any case, the US Constitution can't make "international law" international law, at best it makes a treaty domestic US law.