> It isn't a country and nobody says that it is.

Well, the CIA says it is: https://www.cia.gov/the-world-factbook/countries/holy-see-va...

> The Holy See is sovereign entity with unique status under international law; the status of the Vatican City is derived from the status of the Holy See. It enjoys that status because practically all countries believe that it should do so.

I am only an amateur international lawyer, ask a real one for a more confident answer: but my own understanding is this-the subjects of international law are (1) sovereign states, (2) international organisations established by treaty, (3) sui generis entities; Vatican City is technically an instance of (1) and the Holy See is an instance of (3), and they are technically two distinct subjects of international law, despite having a common sovereign - at least, that’s what I’m pretty sure the Vatican’s own international lawyers will argue… as subjects of international law, both are capable of being parties to treaties, but (generally speaking) the Holy See joins treaties of global interest, Vatican City joins treaties regarding matters of local concern to its own territory. As to where they get this status from, the answer is-customary international law