Make the ChromeOS chromecast system tray integration use a private API.

chrome/common/extensions/api/_api_features.json

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 // This features file defines extension APIs implemented under src/chrome.
 // See extensions/common/features/* to understand this file, in particular
 // feature.h, simple_feature.h, and base_feature_provider.h.
 //
 // Note that specifying "web_page", "blessed_web_page", or "all" as a context
 // type will require manually updating chrome/renderer/resources/dispatcher.cc.
@@ skipping 154 matching lines @@
     "contexts": ["blessed_extension"]
   }],
   "browsingData": {
     "dependencies": ["permission:browsingData"],
     "contexts": ["blessed_extension"]
   },
   "cast.channel": {
     "dependencies": ["permission:cast"],
     "contexts": ["blessed_extension"]
   },
+  "cast.devicesPrivate": {
+    "dependencies": ["permission:cast"],
+    "contexts": ["blessed_extension"]
+  },
   "cast.streaming.rtpStream": {
     "dependencies": ["permission:cast.streaming"],
     "contexts": ["blessed_extension"]
   },
   "cast.streaming.receiverSession": {
     "dependencies": ["permission:cast.streaming"],
     "contexts": ["blessed_extension"]
   },
   "cast.streaming.session": {
     "dependencies": ["permission:cast.streaming"],
@@ skipping 636 matching lines @@
     "internal": true,
     "channel": "stable",
     "dependencies": ["permission:webview"],
     "contexts": ["blessed_extension"]
   },
   "windows": {
     "dependencies": ["api:tabs"],
     "contexts": ["blessed_extension"]
   }
 }