Where did Latin come from?

I think the mistake here is to interpret the Talmud as making a statement about Latin from the perspective of historical linguistics.

I imagine that this is simply a case of establishing legitimacy both over the region (by then completely under Roman control) and the cultural heritage.

In many contexts, language can stand for people or a particular set of religious dicta. E.g. language stands in for 'word of God' or 'commandments'.

The commentary could be quite divergent from the original intent or it could be continuing with the theme of delegitimization. E.g. saying, we are the bearers of the original language with a long line of descent going directly to creation whereas the Latins speak a mongrel language composed of many influences and even had to borrow other people's writing systems.

I'm sure there's some scholarship on this in Talmud studies.