I mean an emperor who didn't know how to speak Latin at all, not only that they would speak greek as their first language.
Did it also signify that latter emperors wouldn't know how to speak Latin? Or was it something more gradual that depended more on the education of the emperor than the time in which he ruled?
Gratitude.
We really do not have that level of detail of knowledge for Byzantine emperors after Heraclius, who most likely spoke some kind of Latin having been in what could still be considered the Late Roman Army. It's definitely not in Theophanes, our goto guy for longer chronologies of middle byzantium.
Anyone after Heraclius, we literally just don't know. We don't know whether emperors after him might have only spoke some latin, or had others translate for them. We don't know whether the main anatolian armies continued to have a mix of latin or was fully greek.
Likely Constans II spoke some Latin considering he tried to move the capital to Siciliy, but after that... no idea.