I think what some sites do is have a visually hidden, not required password field that a password manager can fill in. If it's not a password-based auth, the flow goes to the next step but if it is, it reveals the password field which may already be filled in.
Username enumeration isn't usually considered a vulnerability, but it does make other attacks, like credential stuffing, easier. I.E. you can focus attack resources on usernames that have active accounts.
It's very low on my list of concerns though, usually there's much worse problems when I pentest.