Except you’re giving your passwords in an encrypted format. So if the company is trustworthy, it’s safe to let them store your passwords because it’s encrypted in such a way that even the company who own the password manager couldn’t access your passwords even if they wanted to.

(Note the caveat of “IF the company is trustworthy”, which rules out Lastpass)

Now there are legitimate arguments against storing passwords in the cloud via a password manager… so in that case, you may wish to use a local password manager (like Keepass) instead.