Was Latin spoken in the Byzantine empire, even though the official language was Greek? And did Byzantines study Latin texts?

What Steve Theodore’s answer to Was Latin spoken in the Byzantine empire, even though the official language was Greek? And did Byzantines study Latin texts? said, and what Steve Theodore’s answer to Were the medieval Byzantines familiar with the famous figures of Roman antiquity, like Cato the Elder, Scipio Africanus, or Cincinnatus?  said.

In particular, Steve mentions Maximus Planudes’ translations from Latin. Those weren’t a result of a periodic thaw, those were one-offs at the very end of Byzantium. It was only in the last century of Byzantium, with Byzantium reduced to a bystander,  the Latins ruling much of the Greek-speaking world, and persistent pressure for Church Union, that Byzantine scholars noticed there was anything worthwhile done in the West at all. It was him, Demetrios Kydones, Prochoros Kydones, Gennadius Scholarius, Manuel Holobolos, George Pachymeres. All 13th century or later. And with the exception of Planudes, who did Ovid, they’re all translating Catholic theology and Boethius, not the Classics.