The get_callback
part is generated within the WP_REST_Controller::add_additional_fields_to_object()
method with:
$object[ $field_name ] = call_user_func(
$field_options['get_callback'],
$object,
$field_name,
$request,
$this->get_object_type()
);
That means the callback has four input arguments:
'get_callback' => function ( $object, $field_name, $request, $object_type ) {
// ...
}
and for the requested category object, we can get the term id with:
$term_id = $object['id'];