Add Store+Sync to reading list.

ios/chrome/browser/reading_list/BUILD.gn

 # Copyright 2016 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.
 
 source_set("reading_list") {
   sources = [
     "reading_list_download_service.cc",
     "reading_list_download_service.h",
     "reading_list_download_service_factory.cc",
     "reading_list_download_service_factory.h",
     "reading_list_entry.cc",
     "reading_list_entry.h",
     "reading_list_model.cc",
     "reading_list_model.h",
     "reading_list_model_bridge_observer.h",
     "reading_list_model_bridge_observer.mm",
     "reading_list_model_factory.cc",
     "reading_list_model_factory.h",
     "reading_list_model_impl.cc",
     "reading_list_model_impl.h",
     "reading_list_model_observer.h",
     "reading_list_model_storage.h",
-    "reading_list_model_storage_defaults.h",
-    "reading_list_model_storage_defaults.mm",
+    "reading_list_pref_names.cc",
+    "reading_list_pref_names.h",
+    "reading_list_store.cc",
+    "reading_list_store.h",
+    "reading_list_store_delegate.h",
     "url_downloader.cc",
     "url_downloader.h",
   ]
   deps = [
     "//base",
     "//components/keyed_service/core",
     "//components/keyed_service/ios",
+    "//components/leveldb_proto",
+    "//components/pref_registry",
+    "//components/prefs",
+    "//components/sync",
+    "//components/sync/protocol",
     "//ios/chrome/browser:browser_no_public_deps",
     "//ios/chrome/browser/browser_state",
+    "//ios/chrome/browser/reading_list/proto",
     "//ios/web",
     "//net",
     "//url",
   ]
   public_deps = [
     "//ios/chrome/browser/dom_distiller",
   ]
 }
 
 source_set("unit_tests") {
   testonly = true
   sources = [
     "reading_list_entry_unittest.cc",
-    "reading_list_model_storage_unittest.mm",
     "reading_list_model_unittest.cc",
+    "reading_list_store_unittest.cc",
     "url_downloader_unittest.cc",
   ]
   deps = [
     ":reading_list",
     "//base",
     "//base/test:test_support",
+    "//components/sync:test_support_model",
+    "//components/sync/protocol",
     "//ios/chrome/browser",
     "//ios/chrome/browser/dom_distiller",
+    "//ios/chrome/browser/reading_list/proto",
     "//ios/web:test_support",
     "//testing/gtest",
   ]
 }