Even if some password managers fixed this specific vulnerability I would stop using them because they are all using some type of cloud service.
Good password manager should be open source and option to store everything locally, or by using your own server and encryption.
I would suggest checking out KeePass and some of it's forks.
KeePass is wonderfully great for local use.
And you're right, many of them rely on cloud.
For now I still use bitwarden exactly because it's open source. I need a solution that works on my home PC, my work PC and my mobile too.
And if you really want to, you can probably host your own bitwarden server too. I chose to be more careful in locking the browser extension right after use.