Self-registration with approval
The plugin Self-registration with approval is slightly different from the Email-based self-registration as it requires a Site administrator or another user with the capability auth/approved:approve to approve the registration request before the user is added to the site.
The user registers in the same way as with the Email-based self-registration method and gets an email to confirm their email address. The Site administrator (or another user with the capability listed above) can then go to Site administration > Plugins > Authentication > Self-registration with approval > Pending requests to either approve or reject the user's request. Once this is done, the user will get an email to let them know whether or not they've been approved.