Store user’s registration date as meta

In your case $registered is the user id not the user object so it does not work. Please use the code as given below.

add_action( 'user_register', 'set_user_registration_date', 10, 1 );

function set_user_registration_date( $user_id ) {
    $user = get_userdata ( $user_id );

    // Update the registration meta data
    update_user_meta ( $user_id, 'registration_date', $user->user_registered );
}