Make extensions DSE persistent in browser prefs

chrome/browser/search_engines/template_url_service_factory.cc

Index: chrome/browser/search_engines/template_url_service_factory.cc
diff --git a/chrome/browser/search_engines/template_url_service_factory.cc b/chrome/browser/search_engines/template_url_service_factory.cc
index e2d93663a73bf55fcd25ec68a866ba1fe550c7c7..35cf751e5365fa88da6c5679eff3a3576f3f81b5 100644
--- a/chrome/browser/search_engines/template_url_service_factory.cc
+++ b/chrome/browser/search_engines/template_url_service_factory.cc
@@ -23,6 +23,7 @@
 #include "components/search_engines/default_search_manager.h"
 #include "components/search_engines/search_engines_pref_names.h"
 #include "components/search_engines/template_url_service.h"
+#include "extensions/browser/extension_pref_value_map_factory.h"
 #include "rlz/features/features.h"
 
 #if BUILDFLAG(ENABLE_RLZ)
@@ -58,7 +59,8 @@ std::unique_ptr<KeyedService> TemplateURLServiceFactory::BuildInstanceFor(
       std::unique_ptr<TemplateURLServiceClient>(
           new ChromeTemplateURLServiceClient(
               HistoryServiceFactory::GetForProfile(
-                  profile, ServiceAccessType::EXPLICIT_ACCESS))),
+                  profile, ServiceAccessType::EXPLICIT_ACCESS),
+              ExtensionPrefValueMapFactory::GetForBrowserContext(context))),
       GoogleURLTrackerFactory::GetForProfile(profile),
       g_browser_process->rappor_service(), dsp_change_callback);
 }