Make extensions DSE persistent in browser prefs (Reland)

components/search_engines/default_search_manager.h

Index: components/search_engines/default_search_manager.h
diff --git a/components/search_engines/default_search_manager.h b/components/search_engines/default_search_manager.h
index 94c699a0f0d326eb804521e149034478ae5d690f..975c70e142ca41a982f6faae5b27d10432a46c7d 100644
--- a/components/search_engines/default_search_manager.h
+++ b/components/search_engines/default_search_manager.h
@@ -108,14 +108,6 @@ class DefaultSearchManager {
   // Write default search provider data to |pref_service_|.
   void SetUserSelectedDefaultSearchEngine(const TemplateURLData& data);
 
-  // Override the default search provider with an extension.
-  void SetExtensionControlledDefaultSearchEngine(const TemplateURLData& data);
-
-  // Clear the extension-provided default search engine. Does not explicitly
-  // disable Default Search. The new current default search engine will be
-  // defined by policy, extensions, or pre-populated data.
-  void ClearExtensionControlledDefaultSearchEngine();
-
   // Clear the user's default search provider choice from |pref_service_|. Does
   // not explicitly disable Default Search. The new default search
   // engine will be defined by policy, extensions, or pre-populated data.