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This is a reland of d2d3af26

Also we now call
base::PostTaskAndroid::SignalNativeSchedulerShutdown() which on the
Java side has the following comment
"This is here to make C++ tests work"

Probably a good idea to call it :)

Also we no longer call ResetForTesting() but Shutdown instead. As this
what happens in prod.

Original change's description:
> Fix flakly content_browsertests
>
> Looks like BrowserTaskExecutor is being deleted while the IO thread is
> still running and thus capable of posting tasks. Also  browser tests are
> like prod, we shouldn't manually shut down pools and schedulers.
>
> Bug: 963702
> Change-Id: I1cb953acc4b495631fe269af9e06b94fbe5f2a52
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1628748
> Commit-Queue: Carlos Caballero <carlscab@google.com>
> Reviewed-by: Scott Violet <sky@chromium.org>
> Reviewed-by: Alex Clarke <alexclarke@chromium.org>
> Reviewed-by: Gabriel Charette <gab@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#667097}

Bug: 963702
Change-Id: I88f2b8d418eeb1a9a44f8f17bd5c1147993e8e71
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1651725Reviewed-by: Scott Violet <sky@chromium.org>
Reviewed-by: Gabriel Charette <gab@chromium.org>
Commit-Queue: Carlos Caballero <carlscab@google.com>
Cr-Commit-Position: refs/heads/master@{#682624}