Enable sync for the settings from the Extension Settings API.

chrome/browser/extensions/extension_settings_api.h

 // Copyright (c) 2011 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.
 
 #ifndef CHROME_BROWSER_EXTENSIONS_EXTENSION_SETTINGS_API_H_
 #define CHROME_BROWSER_EXTENSIONS_EXTENSION_SETTINGS_API_H_
 #pragma once
 
 #include "base/compiler_specific.h"
 #include "chrome/browser/extensions/extension_function.h"
@@ skipping 10 matching lines @@
   //
   // Implementations should fill in args themselves, though (like RunImpl)
   // may return false to imply failure.
   virtual bool RunWithStorage(ExtensionSettingsStorage* storage) = 0;
 
   // Sets error_ or result_ depending on the value of a storage Result, and
   // returns whether the Result implies success (i.e. !error).
   bool UseResult(const ExtensionSettingsStorage::Result& storage_result);
 
  private:
-  // Component of RunImpl which runs on the FILE thread.
-  void RunOnFileThread();
+  // Called via PostTask from RunImpl.  Calls RunWithStorage and then
+  // SendReponse with its success value.
+  void RunWithSettingsOnFileThread(ExtensionSettings* settings);
 };
 
 class GetSettingsFunction : public SettingsFunction {
  public:
   DECLARE_EXTENSION_FUNCTION_NAME("experimental.settings.get");
 
  protected:
   virtual bool RunWithStorage(ExtensionSettingsStorage* storage) OVERRIDE;
 };
 
@@ skipping 15 matching lines @@
 
 class ClearSettingsFunction : public SettingsFunction {
  public:
   DECLARE_EXTENSION_FUNCTION_NAME("experimental.settings.clear");
 
  protected:
   virtual bool RunWithStorage(ExtensionSettingsStorage* storage) OVERRIDE;
 };
 
 #endif  // CHROME_BROWSER_EXTENSIONS_EXTENSION_SETTINGS_API_H_