It is not a good to compare the Roman Empire to something that ended in 1912, just 2 years before WW1. Hahahaha. Later empires and their languages: Austrian German vs German. Perhaps something more far ranging: Ukrainian vs Russian. Not Polish since it doesn’t share an alphabet. But maybe Polish in spoken form.

If you want to bring Germanic and Slavic language families into the picture, they are more proto-Indo-European language families, none mutually comprehensible despite common roots. We can also mention the numerous offshoots of Sanskrit in India, chiefly Hindi today, but with many others in use, likewise traced back to proto-Indo-European. (Thus the "Indo" part of the name.)

We can talk about Chinese political unity up into the modern era, but the shared cultural legacy goes back to the classical period, mediated by traditional literature originating in 14th century. Mandarin has long been the language of imperial administration, and has exerted a regularizing influence on local languages without displacing them. Still, it is certainly a very different language from that used to administer empires many centuries ago, despite relying on a common written syllabary. Meanings drift.

The original topic was how people who speak only Mandarin are taught that other Sinitic languages are "just dialects", and are misled by seeing users of these other languages writing in Mandarin, translating as they go; and not understanding the depth of translation involved. This confusion between translation and mere transcription does not seem to occur outside China. The current government prefers the confusion, probably to help enforce a belief in more unity than exists.