That’s right. The United States did not diplomatically recognize the Holy See until Reagan established diplomatic relations in 1984.
The real fun fact is why no diplomatic recognition existed until then: separation of church and state. It was viewed as an unconstitutional violation of the separation of church and state to recognize the Pontificate as a foreign nation. Also, American Protestants were hostile towards the Pope and the Catholic hierarchy and were historically against such recognition.
For much of the 20th century U.S. Presidents would send a personal representative to the Holy See, but they were not an official ambassador until 1984.
History can be surprising and illuminating, no?