Add email addresses to already registered users

Doing This For a Single User In The user_register Filter

Instead of using get_userdata in your filter, fetch the user itself as a WP_User object via get_user_by:

$user = get_user_by( 'id', $user_id );

This gives you access to all of the fields of WP_User directly, e.g.:

echo $user->user_login;

Which you can then plug into your code

Doing this for all the other users

You should use WP_User_Query to fetch an array of users that do not have emails ( assuming the email is an empty string ). This would not happen inside your filter and is a separate independent piece of code.

https://developer.wordpress.org/reference/classes/wp_user_query/

Here’s an example from the docs that loops through every user with a blank email and displays their name:

// The Query
$user_query = new WP_User_Query( [] );

// if users were found
if ( ! empty( $user_query->get_results() ) ) {
    // then for each user
    foreach ( $user_query->get_results() as $user ) {
        // if it already has an email, skip it
        if ( ! empty( $user->user_email ) ) {
            continue;
        }

        // otherwise, add an email here...
    }
} else {
    echo 'No users found.';
}

You can remove the echo and replace it with your check that tests the email is empty and updates the user.

Note that since you have a lot of users, you may need to set 'number' => 200, 'paged' => 1, in the WP_User_Query arguments, and re-run the loop several times with paged set to higher numbers. This is to avoid running out of memory.