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As agreed upon in design doc @
https://docs.google.com/document/d/1tssusPykvx3g0gvbvU4HxGyn3MjJlIylnsH13-Tv6s4/edit?ts=5e1c66d5&pli=1#bookmark=id.ll79iqi5rlpp

base::ThreadPool counterpart to move away from post_task.h is @
https://chromium-review.googlesource.com/c/chromium/src/+/1977964

API usage migration will be done in a follow-up mega CL.
This CL at least uses it in its own tests.

See https://chromium-review.googlesource.com/c/chromium/src/+/2015655
for how this will look in practice for a few callsites.

Bug: 1026641
Change-Id: I98771fd68a513bf0a4776672a8d75fcbbb200bea
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2014055
Commit-Queue: Gabriel Charette <gab@chromium.org>
Reviewed-by: Alexander Timin <altimin@chromium.org>
Reviewed-by: François Doray <fdoray@chromium.org>
Reviewed-by: Darin Fisher <darin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#735734}