Make extensions DSE persistent in browser prefs (Reland)

components/search_engines/template_url_prepopulate_data.h

Index: components/search_engines/template_url_prepopulate_data.h
diff --git a/components/search_engines/template_url_prepopulate_data.h b/components/search_engines/template_url_prepopulate_data.h
index 17c81cd9ff4876ce6163f305d1fde96e611d4354..8f25362fc63a79b0604b16093c932605a6cd960b 100644
--- a/components/search_engines/template_url_prepopulate_data.h
+++ b/components/search_engines/template_url_prepopulate_data.h
@@ -42,6 +42,10 @@ std::vector<std::unique_ptr<TemplateURLData>> GetPrepopulatedEngines(
     PrefService* prefs,
     size_t* default_search_provider_index);
 
+// Returns the prepopulated search engine with the given |prepopulated_id|.
+std::unique_ptr<TemplateURLData> GetPrepopulatedEngine(PrefService* prefs,
+                                                       int prepopulated_id);
+
 #if defined(OS_ANDROID)
 // Returns the prepopulated URLs associated with |locale|, if it differs from
 // the current country.  |locale| should be a two-character uppercase ISO 3166-1