Make SearchBox use per-frame task runner for incoming mojo messages

Currently SearchBox is using the default per-thread task runner for its
mojo bindings. We are converting it to use per-frame task runner so that
BFCache can freeze the task runner correctly and don't need to evict
the page in case it receives mojo messages for SearchBox.

Change-Id: I16ddd7a19b4da0fec3eba61318e8901cb210b7af
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1877488
Commit-Queue: Rakina Zata Amni <rakina@chromium.org>
Reviewed-by: Hajime Hoshi <hajimehoshi@chromium.org>
Reviewed-by: Kouhei Ueno <kouhei@chromium.org>
Reviewed-by: Alexander Timin <altimin@chromium.org>
Reviewed-by: Dan Beam <dbeam@chromium.org>
Cr-Commit-Position: refs/heads/master@{#709340}

chrome/renderer/searchbox/searchbox.cc

@@ -210,9 +210,14 @@ SearchBox::SearchBox(content::RenderFrame* render_frame)
   mojo::AssociatedRemote<chrome::mojom::EmbeddedSearchConnector> connector;
   render_frame->GetRemoteAssociatedInterfaces()->GetInterface(&connector);
   chrome::mojom::EmbeddedSearchClientAssociatedPtrInfo embedded_search_client;
-  binding_.Bind(mojo::MakeRequest(&embedded_search_client));
-  connector->Connect(mojo::MakeRequest(&embedded_search_service_),
-                     std::move(embedded_search_client));
+  binding_.Bind(mojo::MakeRequest(&embedded_search_client),
+                render_frame->GetTaskRunner(
+                    blink::TaskType::kInternalNavigationAssociated));
+  connector->Connect(
+      mojo::MakeRequest(&embedded_search_service_,
+                        render_frame->GetTaskRunner(
+                            blink::TaskType::kInternalNavigationAssociated)),
+      std::move(embedded_search_client));
 }
 
 SearchBox::~SearchBox() = default;