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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}