Very realistic to believe that some of the Second Temple treasures are in the Vatican vaults.
I don't find it realistic at all. Actually, unless the crusaders found it (which I doubt as I will explain below), I find this rumour rather absurd, if not plain ridiculous ...
We know from historical sources that, although brought to Rome after the destruction of the second temple by Titus (by the way a long time before the Vatican was built), the sacred treasures from the Jerusalem Temple were later pillaged by the Wisigoths and Vandals (who captured Rome in the 5th century), who took the Menorah to Carthage. Please bear in mind that although converted to Christianity, the Vandals were Arian. So they were absolutely not friends of the Catholic Pope, who by the way, was at that time a relatively weak local bishop. In other words, the Vandals had no reason whatsoever to leave him with any significant treasure, especially since the poor guy was on the loser's side ...
Procopius says that Belisarius took the Menorah (and possibly the other treasures) back to Constantinopolis when he conquered Africa. He proceeds to claim that Justinian almost immediately sent it back to Jerusalem.
Although I forgot the reference, I am also pretty sure I've read somewhere that an Arab traveller from the Middle Ages claimed that he had seen the Menorah in Egypt later on ...
So the likeliness of the Temple treasures ending in a Vatican vault is really, really small ... I am sure that Da Vinci Code fans and adepts of the theory that "the Catholic Church is the empire of Evil" will disagree, but that's not history, but fantasy.
Here an interesting article on the topic :
https://library.biblicalarchaeology.org/article/did-the-temple-menorah-come-back-to-jerusalem/
Now one may say that even if the Menorah was taken back to Jerusalem : (1) it doesn't imply that the other treasures and notably the Ark was taken along, (2) that the Vatican did not find a way to take it back later on. So let's examine these points :
The crusaders could have found the treasures back when they conquered Jerusalem. However, why would they have hidden such a discovery to the public in a time where Holy Land relics were in high demand in the whole of Europe ? Please remember that it was a time when crusaders ostentatiously brought back pieces of the Holy Cross and of the Crown of Spines from the East. So for what weird reason would crusaders have had to hide their finding of the old Temple's treasures ? That's incoherent, hence most unlikely.
Now, for the lost Ark. Yes, if taken along the Menorah to Rome by Titus (if it hadn't vanished before), it could indeed have followed another path. But then, if we go back to the facts, the text of the Bible quoted above : it was mainly made of wood coated with gold. Wood is a perishable material in moist climates. If it was brought to Rome, it might have decayed over the centuries. With the Ark's core gone, all what might have remained would have been the gold coating and the contents. For ancient pagan Romans, the content might have been considered worthless and dumped. The temptation would then have been heavy for whomever got his hands on the rest to smelt the coating for coins or other metallurgic purposes. So if the wooden Ark got to Rome, its most likely fate would have been to be smelted as there was no point in keeping it as a piece of rubble.
Of course, it might never have been taken to Rome in the first place. But in that case, it would be even more unlikely to find it in the Vatican "vaults".
