An article in The Jerusalem Post is quite interesting.
https://www.jpost.com/jerusalem-report/article-696068
According to Vatican expert Dr. Michael A. Calvo, those vessels and others found their way to the Vatican via another route, after making their way to Byzantium: “These include Temple candelabra given to Pope Innocent III by Baldwin I after the sacking of Constantinople and the massacre of the Christian Orthodox population,” Calvo claims. “Temple shofars and utensils; garments of the High Priest; the Tzitz – a gold plaque with the words Kodesh L’Hashem (“Holy to the Lord”); cultural objects, and many other objets d’art, books and manuscripts that the Vatican and other churches have appropriated and placed in their own storerooms, libraries, and museums.”
Late that night, and after much spiritual preparation, the rabbi met the guard at the Vatican gates, with his students remaining outside, and went down the steps (four stories under St. Peter’s Museum) to a hidden maze of ancient galleries attached to the Necropolis. After finally reaching the cave entrance, he saw what he saw, and writes in his book of Responsa that he saw “enough,” and was not capable of seeing anymore. He then turned around and practically ran out of the building.