You should use a local-storage password manager, like KeePass.
I feel like this is part of the reason we need real data protection laws in the US. There doesn't seem to be any downside for a company with lax security practices.
I intentionally don't let the clients integrate with the browser. I let the browser itself cache the unimportant stuff for convenience, and anything important I always paste from the password manager and have to get a code from the totp app also anyway.
I don't think anyone should use a fully 3rd party full featured password manager like lastpass or onepass.
I would say it is NOT better that they use that vs nothing. 'anything is better than nothing' is not true here. Some things are better than nothing, and some are not.