And, as a follow-up, is the Holy See the only still-operational institution founded by the Romans (Original Roman Republic and Empire, as opposed to Byzantium, Holy Rome or Gothic Italy)?
Can we get some additional clarification here?
The Orthodox church would be on your list if the Holy See is since they were "technically" founded at the same time. Also the Roman church didn't suffer the great schism until 1054, which was well in the "Byzantium" period so Byzantium was not a successor to Rome is was Rome, historians only started referring to it as Byzantium (Greek Rome) in the mid 19th century, there was no disruption, as the the entire government of Rome had moved to Constantinople in 330, The city of Rome didn't fall until 476.