Is the Demon Slayer manga actually finished?

The manga's been complete for a while now — Gotouge ended it back in 2020, 205 chapters collected into 23 volumes. So everything since then, Mugen Train, Entertainment District, Swordsmith Village, and now the Infinity Castle films, is the anime working through material that already exists and already has an ending. Nothing new is being written alongside it.

It's a nice position to be in as a viewer honestly. You can look up how much story is left whenever you want to gauge pacing, and there's no risk of the anime ever catching up to an unfinished story the way something like My Hero Academia eventually will.