Enable sync for the settings from the Extension Settings API.

chrome/browser/sync/protocol/extension_setting_specifics.proto

+// 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.
+//
+// Sync protocol datatype extension for an extension setting.
+
+// Update proto_value_conversions{.h,.cc,_unittest.cc} if you change
+// any fields in this file.
+
+syntax = "proto2";
+
+option optimize_for = LITE_RUNTIME;
+option retain_unknown_fields = true;
+
+package sync_pb;
+
+import "sync.proto";
+
+// Properties of extension setting sync objects.
+message ExtensionSettingSpecifics {
+  // Id of the extension the setting is for.
+  optional string extension_id = 1;
+
+  // Setting key.
+  optional string key = 2;
+
+  // JSON value of setting.
+  optional string value = 3;
+}
+
+extend EntitySpecifics {
+  optional ExtensionSettingSpecifics extension_setting = 96159;
+}