Enable sync for the settings from the Extension Settings API.

chrome/browser/extensions/extension_settings_api.cc

 // 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.
 
 #include "base/bind.h"
 #include "base/values.h"
 #include "chrome/browser/extensions/extension_service.h"
 #include "chrome/browser/extensions/extension_settings_api.h"
 #include "chrome/browser/profiles/profile.h"
 
@@ skipping 25 matching lines @@
 
 // SettingsFunction
 
 bool SettingsFunction::RunImpl() {
   profile()->GetExtensionService()->extension_settings()->GetStorage(
       extension_id(),
       base::Bind(&SettingsFunction::RunWithStorage, this));
   return true;
 }
 
-void SettingsFunction::RunWithStorage(ExtensionSettingsStorage* storage) {
+void SettingsFunction::RunWithStorage(
+    SyncableExtensionSettingsStorage* storage) {
   // Mimic how RunImpl() is handled in extensions code.
   if (!RunWithStorageImpl(storage)) {
     SendResponse(false);
   }
 }
 
 // Concrete settings functions
 
 bool GetSettingsFunction::RunWithStorageImpl(
     ExtensionSettingsStorage* storage) {
@@ skipping 41 matching lines @@
   }
 
   return true;
 }
 
 bool ClearSettingsFunction::RunWithStorageImpl(
     ExtensionSettingsStorage* storage) {
   storage->Clear(new StorageResultCallback(this));
   return true;
 }