How to save one API response to WooCommerce order meta data

You’re very close.

$order->update_meta_data() will update the meta value inside the $order object, but it will not store the change in the database. To save changes to a WooCommerce CRUD object you need to run the save() method:

if ( $response_code == 200 )  {
    $order->update_meta_data( 'token_received_key', $token );
    $order->save();
}