Do they send diplomats to any other religion? It’s silly to pretend the Vatican is a nation. Thats only because of a deal with Mussolini in the 20s. We didn’t recognize it and send an ambassador until the Reagan era, and that was for Cold War reasons back when the pope was catholic and not a communist.
We need to get back to where it was before.
One reason many countries maintain diplomatic relations with Vatican City, is that since it is worldwide and has ambassador from many countries it is an excellent place to gather information and to pass on information. The US has had consular relations with the Holy See since 1797, there was a lapse of some years after the Civil War.