I can’t get a return value from Ajax

by

Returning the result array will only return to the PHP function calling it, instead you actually need to output it by echoing it, and in this case because it is an array, encoding it with JSON before outputting. So return $result becomes:

echo json_encode($result); exit;

and then add dataType to the javascript call so it can recognize the array data:

    var data = {
        'action': 'smsgte_admin_send',
        'message': message,
        'security': smsgte_Ajax.ajax_nonce,
        'dataType': 'json'
    };

See this answer for a more complete example:
https://stackoverflow.com/a/8823995/5240159