I ran into the same problem and ended up building a browser extension to solve it. The main issue for me was enforcing a properly formatted commit message in the Bitbucket UI during a merge or squash. Since we squash our commits, that final message really needs to follow the conventional commit format.
As far as I can tell, Bitbucket doesn’t support plugins for customizing the merge UI, so a browser extension was the only workaround I could come up with.