The common (trade) tongue is Latin. In the Empire, pretty much everyone regardless of caste (including the Ardu) can speak Latin, plus whatever regional dialect is local to them.
The Mushkenu (middle class) of the Empire were literate in the common tongue as well. This was one of the defining features of the Mushkenu, in fact. So, scholars and scribes and teachers may be penniless servants, but they won’t be Ardu (serfs).
The Amelu (nobility) of the Empire spoke Parsik fluently, spoke the common tongue easily, and can converse in their local regional dialects as necessary. They were literate in both Parsik and Common.
The Holy Church rites and scriptures were in Parsik. This doesn’t make clerics and priests Amelu, but it does give them a leg up on the other Mushkenu in social standing.
Note that for the 95% of Imperial citizens who never left their home town, everybody would already know what your social class was by your family regardless of qualification.