Email Notification to new roles

Hello,

I’m looking for a snippet that would help me to send an email notification to users when a new role is added to their profile.

I found a snippet that works fine if I want to change the default role, but if I add another role nothing is sent.

Here is the snippet I use :

function notify_user_on_role_change($user_id,$old_user_data,$userdata) {
    // Getting role before update
    foreach($old_user_data->roles as $role):
        $old_role = $role;
    endforeach;

    // error_log(print_r($userdata,true)); // debug 

    //If we change role send email
    if($old_role != $userdata['role']):
        $user_info = get_userdata( $user_id );
        $to = $user_info->user_email; 
        $subject = "Profile Updated";
        $message = "Hello, your user role is changed to ".$userdata['role']."";
        wp_mail( $to, $subject, $message);
    endif;
}
add_action('profile_update','notify_user_on_role_change',10,3);

Thanks for your help !
Jennifer