Change `/google_api/authorizations/` to `/google_api/auth/`.

app/controllers/google_api/authorizations_controller.rb

@@ -2,7 +2,7 @@ module GoogleApi
   class AuthorizationsController < ApplicationController
     def callback
       token, expires_at = GoogleApi::CloudPlatform::Client
-        .new(nil, callback_google_api_authorizations_url)
+        .new(nil, callback_google_api_auth_url)
         .get_token(params[:code])
 
       session[GoogleApi::CloudPlatform::Client.session_key_for_token] = token

app/controllers/projects/clusters_controller.rb

@@ -17,7 +17,7 @@ class Projects::ClustersController < Projects::ApplicationController
   def login
     begin
       @authorize_url = GoogleApi::CloudPlatform::Client.new(
-        nil, callback_google_api_authorizations_url,
+        nil, callback_google_api_auth_url,
         state: namespace_project_clusters_url.to_s).authorize_url
     rescue GoogleApi::Auth::ConfigMissingError
       # no-op

config/routes/google_api.rb

 namespace :google_api do
-  resource :authorizations, only: [], controller: :authorizations do
+  resource :auth, only: [], controller: :authorizations do
     match :callback, via: [:get, :post]
   end
 end