Make extensions DSE persistent in browser prefs

components/search_engines/BUILD.gn

Index: components/search_engines/BUILD.gn
diff --git a/components/search_engines/BUILD.gn b/components/search_engines/BUILD.gn
index 2ca2e4ae1c720790abde5e37c461dc2e4411b9df..61411229997391ca532e24a8991d62c6d38da08b 100644
--- a/components/search_engines/BUILD.gn
+++ b/components/search_engines/BUILD.gn
@@ -96,6 +96,8 @@ static_library("search_engines") {
 static_library("test_support") {
   testonly = true
   sources = [
+    "search_engines_test_util.cc",
+    "search_engines_test_util.h",
     "testing_search_terms_data.cc",
     "testing_search_terms_data.h",
   ]
@@ -103,6 +105,7 @@ static_library("test_support") {
   public_deps = [
     ":search_engines",
     "//base",
+    "//components/sync_preferences:test_support",
     "//testing/gtest",
   ]
 }