Yes, the idea of empire as being something bigger than a kingdom is a popular misunderstanding.

However, Rome (and Byzantium) were actually very good at integrating conquered populations into their culture.

Very early in the empire, a law made all conquered people officially Roman, with all the benefits and protections it entailed.

After 2-3 generations, there was not much difference between a Roman from Gaul and a Roman from Rome: they spoke the same language, worshipped the same gods, had the same education, and viewed themselves as Roman. And critically, the Romans from Rome didn't see their compatriots from elsewhere as different.

The Senate was composed entirely of men, but apart from that it was a DEI dream. Some of the emperors were dark-skinned, originating from current Syria: we only know because of their genealogy, their portraits, but otherwise no one cared enough to mention their skin colour, especially in a negative way.

To such an extent that, for most of their existence, Rome and Byzantium did not actually fit the definition of empire.