Many countries including the US have diplomatic relations with “the Holy See”, not with “the Vatican”. Even if Italy or the EU should revoke the agreement between Italy and the Holy See, and seize the territory we now call the Vatican, that would not alter the diplomatic relations of the Holy See. The Holy See maintained diplomatic relations with some countries, or some degree of sovereignty, during the time when the popes lived in Avignon France, and even during the decades prior to the 1920’s concordat with Italy, when the Pope was a sovereign with no territory.
But the deeper issue is that the media misuses the term “Vatican” as “do you want to follow your conscience, or the Holy Spirit, or instead be a robot for the (foreign) Vatican”? In the 1970s anti-Catholics would call for an “American Catholic Church” which would make our own liturgy, ordain women, ok contraception, divorce/remarriage ok, maybe replace “God, the Father” as sexist, etc, as opposed to obeying elderly white men in the Vatican, who don’t understand our ways. Thank God that trend is mostly disappearing, as the bishops are increasingly united with the Holy See, and the laity, in opposing secularism.