Hi James,
$response[] = will create (if it doesn't exist) or append the right-hand value to the $response array. So if $html->data->identifier is a simple string, e.g. 'Price', then a new array would be ['Price'] or array(0=>'Price')
$order->get_items() appears to be a nested object not an array. I've created a copy and iterated through it below.
$obj = (object) array(365 => (object) array('name'=>'steel wool 3', 'qty' => 1) );
//print_r($obj);
foreach($obj as $key => $obj2) {
foreach($obj2 as $key => $value) {
echo $value.'<br>';
}
}