I think Latin in a surviving Roman Empire might end up like OTL's Chinese. A bunch of different dialects that are often different enough to be considered separate languages all lumped under the umbrella of Latin, with a standardized Latin language being the lingua franca, similar to Mandarin. That's not even factoring in Greek or Coptic, which would be major languages in a surviving Roman Empire assuming it had the borders it had at its peak.Some form of modern Latin most likely
this even though in reality it would be a the dialects that would slowly die off ( once standardization comes) with other major language families ( depending of the pod) mainly the slavic ones and armenianA surviving Roman Empire is more likely to be the ERE. So Greek.