PHP - Google API (Beta) getting bearer token - php

Question

I have been using the Google API client in PHP for a project with google assistant where I need to post transaction updates.
See : https://developers.google.com/actions/transactions/dev-guide-physical-custom#6_send_order_updates
I use the server-to-server procedure to connect : https://developers.google.com/api-client-library/php/auth/service-accounts
I didn't found any support for Transactions or Actions. So I can't just call a service like the example. My goal is just to get the bearer token back and code the update based on the documentation of the transactions.
So I made this code :
$client = new Google_Client();
putenv('GOOGLE_APPLICATION_CREDENTIALS='.'path/to/file/');
$client->useApplicationDefaultCredentials();
$client->setApplicationName('Update_Orders_Test');
$client->setScopes(['https://www.googleapis.com/auth/actions.fulfillment.conversation']);
$auth = $client->authorize();
But with this code I can't get the bearer token in the $client object or the $auth object. But I do not have any error too. The path to the JSON file is correct, there is an error if the file doesn't exist.
Here is the client object :
{
"auth": null,
"http": {},
"cache": {},
"token": null,
"config": {
"application_name": "Update_Orders_Test",
"base_path": "https://www.googleapis.com",
"client_id": "",
"client_secret": "",
"redirect_uri": null,
"state": null,
"developer_key": "",
"use_application_default_credentials": true,
"signing_key": null,
"signing_algorithm": null,
"subject": null,
"hd": "",
"prompt": "",
"openid.realm": "",
"include_granted_scopes": null,
"login_hint": "",
"request_visible_actions": "",
"access_type": "online",
"approval_prompt": "auto",
"retry": [],
"cache_config": [],
"token_callback": null,
"jwt": null
},
"logger": null,
"deferExecution": false,
"requestedScopes": [
"https://www.googleapis.com/auth/actions.fulfillment.conversation"
]
}
As you can see the basic information are set but not the one relative to the json file.
Is there something I did wrong with this code ?