The Byzantine Empire was Greek. Heraclius changed the official language to Greek already in the 7th century because that’s what everyone spoke.
They kept calling themselves Romans, but they spoke, wrote, and governed in Greek.
They kept calling themselves Romans, but they spoke, wrote, and governed in Greek.
Moreover you're picking a date hundreds of years into the eastern empire's existence and declaring "because they switched official languages hundreds of years later, they were always Greek". Time doesn't flow like that.
Moreover the roman empire, pre-split, spoke quite a bit of this language (well, Koine Greek, the predecessor to Romaic). Including in official communications (particularly in the east), and at least one emperor's private diaries [1].