Not sure what exactly you are trying to do, to be honest, but you are
searching for a Page in your first call and you will get the correct IDs
for that page for sure.
The second call (/me) has no relation to Facebook Pages, it´s for
requesting data of the User profile for the authorized User. And you will
only get "App Scoped IDs" for those.
In order to get data of the Pages in the search result, this is what you
would need to do (i guess, because i don´t know Laravel):
$fb = $this->oauth->consumer('Facebook');
$page = json_decode($fb->request('/662139753894064'), true);