[TaskbarIconFinder] Replace usage of base::Thread by post_task.h

post_task.h is now preferred over using dedicated base::Threads.

Furthermore, this code is preventing PlatformThread::Join() called by
Thread::Stop()) from being marked as a blocking operation in
https://chromium-review.googlesource.com/c/chromium/src/+/1324370.

This code was really only spinning up a thread to run a single task in
an MTA environment. All threads in the TaskScheduler (in the browser
process) are in an MTA.

R=grt@chromium.org

Bug: 707362
Change-Id: I5defbaeefc291f4b417c142cda60918a4cfd471d
Reviewed-on: https://chromium-review.googlesource.com/c/1338221
Commit-Queue: Gabriel Charette <gab@chromium.org>
Reviewed-by: Greg Thompson <grt@chromium.org>
Cr-Commit-Position: refs/heads/master@{#608829}
1 file changed