Is the inline classes feature stable enough for production use?

Depends on what you mean by stable. It’s stable as in it works and works well. But it’s unstable as in “The design of inline classes is experimental, meaning that this feature is moving fast and no compatibility guarantees are given.” https://kotlinlang.org/docs/reference/inline-classes.html

There are still some bugs.

I've tried it a couple of times but got bogged down by bugs (that I reported of course).

I use it, but keep some red tape around bugs (tests that are failing). It is OK for experimental code, but for commercial production - probably not.