Google API - invalid_request - 无法根据请求确定客户端 ID

Question

我正在将 google play 应用内订阅集成到我的应用程序中。要访问 google API，首先我需要获取 access_token，然后在标头中使用它来访问订阅 API。按照程序（Android：inApp购买收据验证google play）我得到了我的凭据文件，如下所示

{
  "type": "service_account",
  "project_id": "my-project-id",
  "private_key_id": "x",
  "private_key": "-----BEGIN PRIVATE KEY-----y-----END PRIVATE KEY-----\n",
  "client_email": "google-play-developer@z.iam.gserviceaccount.com",
  "client_id": "x",
  "auth_uri": "https://accounts.google.com/o/oauth2/auth",
  "token_uri": "https://oauth2.googleapis.com/token",
  "auth_provider_x509_cert_url": "https://www.googleapis.com/oauth2/v1/certs",
  "client_x509_cert_url": "https://www.googleapis.com/robot/v1/metadata/x509/google-play-developer%40y.iam.gserviceaccount.com"
}

注意：真实的 id 和值替换为 x、y 和 z

接下来，为了用 JWT 交换 access_tokenm，我正在使用 php 的 Google API 客户端库 https://github.com/googleapis/google-api-php-client

这是我的代码

$client = new \Google_Client();
$client->setAuthConfig('client_secret.json');
$client->addScope('https://www.googleapis.com/auth/androidpublisher');
$client->setRedirectUri($request->redirect_uri);
$token = $client->fetchAccessTokenWithAuthCode($request->code);

但我无法获取访问令牌。出现以下错误

{
    "error": "invalid_request",
    "error_description": "Could not determine client ID from request."
}