Could it be that you weren't using it correctly? KeePass database files aren't supposed to remain open (for security of course) and it has quite a number of options to automatically close it after certain amount of time or when the window isn't focus, computer is locked, etc. This would trigger a sync with the (NC) server and assuming that all your clients follow the same usage pattern and close the DB after a small window of time, there shouldn't be any conflict.
> NextCloud to be always up of course, also self-hosted
You could use NextCloud's own hosting. But then Bitwarden's server needs to always be up too, and optionally self-hosted.
> Bitwarden just works
A low bar to recommend a password manager, don't you think so?