Automatic registration on main site upon user registration on Multisite

You can hook to wpmu_activate_user and add the user’s role on the main site.

add_action( 'wpmu_activate_user', 'wpse363445_add_user_to_main_site' );
function wpse363445_add_user_to_main_site( $user_id ) {
    if ( is_main_site() ) {
        // Don't run if we're already on the main site.
        return;
    }
    if ( is_user_member_of_blog( get_main_site_id(), $user_id ) ) {
        // Don't add the user to the main site if they're already a member.
        return;
    }
    add_user_to_blog( get_main_site_id(), $user_id, 'subscriber' );
}

References

• wpmu_activate_user hook
• is_main_site()
• add_user_to_blog()
• get_main_site_id()
• is_user_member_of_blog()

Note: This will only work for users that get sent an activation email. If you manually add a user to a site, and opt to not send them an activation email, you’ll need to add them to the main site manually.