I have run into this problem and cant find a simple working php example online that can set the object cache-control while uploading to google cloud storage. I know its a setMet
I think you want to call the setCacheControl function.
Here is a working example:
$bucket_name = 'my-bucket';
$file = "xxx.html";
$infotowrite = "999";
$service = new Google_Service_Storage($client);
$obj = new Google_Service_Storage_StorageObject();
$obj->setName($file);
$obj->setCacheControl('public, max-age=6000');
$results = $service->objects->insert(
$bucket_name,
$obj,
['name' => $file, 'mimeType' => 'text/html', 'data' => $infotowrite, 'uploadType' => 'media']
);