Enable sync for the settings from the Extension Settings API.

chrome/browser/extensions/extension_settings_api.cc

Index: chrome/browser/extensions/extension_settings_api.cc
diff --git a/chrome/browser/extensions/extension_settings_api.cc b/chrome/browser/extensions/extension_settings_api.cc
index 71679018b7711f7b2df0f2380c53aff7f7ba19a2..49a6e0166f6eccdb510e483f4446921168ff84e3 100644
--- a/chrome/browser/extensions/extension_settings_api.cc
+++ b/chrome/browser/extensions/extension_settings_api.cc
@@ -16,18 +16,16 @@ const char* kUnsupportedArgumentType = "Unsupported argument type";
 // SettingsFunction
 
 bool SettingsFunction::RunImpl() {
-  BrowserThread::PostTask(
-      BrowserThread::FILE,
-      FROM_HERE,
-      base::Bind(&SettingsFunction::RunOnFileThread, this));
+  profile()->GetExtensionService()->extension_settings()->RunWithStorage(
+      extension_id(),
+      base::Bind(&SettingsFunction::RunWithStorageOnFileThread, this));
   return true;
 }
 
-void SettingsFunction::RunOnFileThread() {
+void SettingsFunction::RunWithStorageOnFileThread(
+    ExtensionSettingsStorage* storage) {
   DCHECK(BrowserThread::CurrentlyOn(BrowserThread::FILE));
-  ExtensionSettings* settings =
-      profile()->GetExtensionService()->extension_settings();
-  bool success = RunWithStorage(settings->GetStorage(extension_id()));
+  bool success = RunWithStorage(storage);
   BrowserThread::PostTask(
       BrowserThread::UI,
       FROM_HERE,