This is probably a dumb question and I’m missing something but is there any way to select only games that have been completed when browsing?

try with status "released"
https://itch.io/games/released

However, the status is set manually by each developer at the time of publishing, so there is no guarantee that 100% of the games respect it. I clarify this because there are surely episodic or incomplete games that people have given the status of "released"