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I created a new class, BrowserThreadUtils, in content_public/browser. It
has all of the functionalities of base/ThreadUtils that we want to
retain, but uses PostTask. Running blocking tasks has been moved to
a new class TestThreadUtils, because it is not supposed to be used by
production code.

This is part of an ongoing effort to unify Java and C++ scheduling:
http://go/migrating-threadutils-to-posttask

Bug: 863341
Change-Id: Id7da815b63dd2f5c57b01a093401e1c73a5d57db
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1489243
Commit-Queue: Karolina Soltys <ksolt@chromium.org>
Reviewed-by: Bo <boliu@chromium.org>
Reviewed-by: Sami Kyöstilä <skyostil@chromium.org>
Auto-Submit: Karolina Soltys <ksolt@chromium.org>
Cr-Commit-Position: refs/heads/master@{#638208}