> For the biggest differences: by the time of Basil II they were speaking Greek instead of Latin

That isn't a difference. There was never a time when they were speaking Latin.

The Romans, over in Italy, spoke Latin, but the Anatolians, in Turkey, never did. They spoke Greek before any contact with the Romans and they continued to speak Greek long after the Romans were gone.

> it's like the Ship of Theseus, all those changes add up over time.

The Ship of Theseus is more about changes that don't add up over time. If I repair a hole in the ship, it's still the same in pretty much all useful senses of "being the same", and the question is whether a set of changes like that which end up covering the entire ship still leave the whole ship "the same".

If I repair a hole in the ship by replacing it with part of an 18th-century ironclad, and as damage to the wood accrues I just build an ironclad over where the ship used to be, no one is going to think I'm posing some kind of deep question when I ask whether, at the end of the process, I still have the same ship.