[Extensions] Convert some ChromeSyncExtensionFunctions

chrome/browser/extensions/api/omnibox/omnibox_api.h

Index: chrome/browser/extensions/api/omnibox/omnibox_api.h
diff --git a/chrome/browser/extensions/api/omnibox/omnibox_api.h b/chrome/browser/extensions/api/omnibox/omnibox_api.h
index d49ecc1f2809752154bc031920537ed0f69c5c9a..0967893794547259bc9dba52b7a15c7ef1d817e9 100644
--- a/chrome/browser/extensions/api/omnibox/omnibox_api.h
+++ b/chrome/browser/extensions/api/omnibox/omnibox_api.h
@@ -73,7 +73,7 @@ class ExtensionOmniboxEventRouter {
   DISALLOW_COPY_AND_ASSIGN(ExtensionOmniboxEventRouter);
 };
 
-class OmniboxSendSuggestionsFunction : public ChromeSyncExtensionFunction {
+class OmniboxSendSuggestionsFunction : public UIThreadExtensionFunction {
  public:
   DECLARE_EXTENSION_FUNCTION("omnibox.sendSuggestions", OMNIBOX_SENDSUGGESTIONS)
 
@@ -81,7 +81,7 @@ class OmniboxSendSuggestionsFunction : public ChromeSyncExtensionFunction {
   ~OmniboxSendSuggestionsFunction() override {}
 
   // ExtensionFunction:
-  bool RunSync() override;
+  ResponseAction Run() override;
 };
 
 class OmniboxAPI : public BrowserContextKeyedAPI,
@@ -150,7 +150,7 @@ class OmniboxAPI : public BrowserContextKeyedAPI,
 template <>
 void BrowserContextKeyedAPIFactory<OmniboxAPI>::DeclareFactoryDependencies();
 
-class OmniboxSetDefaultSuggestionFunction : public ChromeSyncExtensionFunction {
+class OmniboxSetDefaultSuggestionFunction : public UIThreadExtensionFunction {
  public:
   DECLARE_EXTENSION_FUNCTION("omnibox.setDefaultSuggestion",
                              OMNIBOX_SETDEFAULTSUGGESTION)
@@ -159,7 +159,7 @@ class OmniboxSetDefaultSuggestionFunction : public ChromeSyncExtensionFunction {
   ~OmniboxSetDefaultSuggestionFunction() override {}
 
   // ExtensionFunction:
-  bool RunSync() override;
+  ResponseAction Run() override;
 };
 
 // If the extension has set a custom default suggestion via