> but what about when the existing codebase is already inconsistent?

Then you get people together to agree what consistent looks like.

I find the easiest way to do this is to borrow someone else's publicly documented coding conventions e.g. Company ABC.

Then anyone disagreeing isn't disagreeing with you, they're disagreeing with Company ABC, and they (and you) just have to suck it up.

From there on in, you add linting tools, PR checks etc for any new code that comes in.