Working just as expected

1) You creating group “NotifiedByEmail”, adding users to it.
2) Memorize ID of that group
3) Writing function:

function getNotifiedUsersEmails()
{
    // 2 - is the ID of group
    $group = new Groups_Group( 2 );
    $users = $group->users;
    $emails = [];
    if (!$users) $users = [];
    foreach($users as $user)
    {
        $email = $user->user->data->user_email;
        $emails[] = $email;
    }
    return $emails;
}

4) And use it to send some notification emails only to users that are in a group:

 $emails = getNotifiedUsersEmails();
    
    foreach($emails as $email)
    {
        wp_mail( $email, $subject, $message, $headers );
    }