It happens to me very regularly that a password in my password manager is needed on a different domain. Maybe the logon process is at id.domain.com and password is pinned to domain.com, or maybe the password was created at signup.domain.com and so it doesn't pop up on domain.com, or you have to log in to a hotel's site with the password from their reward scheme (different domain), etc...

In any case users are trained by the internet to need to search for the right password outside the pinned domains. Most of the time I guarantee people don't add the extra domains to the password records. So when a phishing site pops up they'll do the same: search for the site name/domain that they think they're logging into and go from there.

Password managers solve password reuse, weak passwords, etc. but IMO do not solve phishing, especially not for the kind of user who's most susceptible t it (little technical understand, hates this stuff, just wants to follow instructions and not deal with it), but passkeys might.