Follow #29522
Administrators should be able to set a user's email address even if the
email address is not in `EMAIL_DOMAIN_ALLOWLIST`
(cherry picked from commit 136dd99e86eea9c8bfe61b972a12b395655171e8)
Fixes#28660
Fixes an admin api bug related to `user.LoginSource`
Fixed `/user/emails` response not identical to GitHub api
This PR unifies the user update methods. The goal is to keep the logic
only at one place (having audit logs in mind). For example, do the
password checks only in one method not everywhere a password is updated.
After that PR is merged, the user creation should be next.