Deprecate content::BrowserThread::PostAfterStartupTask

BEST_EFFORT tasks will not run until after startup and only if there is no
critical work pending.

This patch should not change the current behaviour. Please double check
whether the task being posted via BrowserThread::PostAfterStartupTask
really cares about being run after startup or just wants to run after
any critical work was completed. If you are fine with it just running
after critical work has completed LGTM and keep on with your life. If
that is not the case let me know and please explain your reasoning in a
comment.

More details:
https://docs.google.com/document/d/1P8PV1qX2cOR2WRFD6v9CjygJkE_mftCtJ7BoqQHCKZI

This CL was uploaded by git cl split.

R=chrisha@chromium.org

Bug: 887407
Change-Id: Ib35383c1272e2ab649ec2b0d76e2b1c9f5f28d88
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1632221Reviewed-by: Chris Hamilton <chrisha@chromium.org>
Commit-Queue: Carlos Caballero <carlscab@google.com>
Auto-Submit: Carlos Caballero <carlscab@google.com>
Cr-Commit-Position: refs/heads/master@{#664699}

chrome/browser/win/conflicts/module_inspector.cc

@@ -106,8 +106,8 @@ ModuleInspector::ModuleInspector(
           base::FeatureList::IsEnabled(kDisableBackgroundModuleInspection)),
       test_connector_(nullptr),
       weak_ptr_factory_(this) {
-  // Use PostAfterStartupTask to be notified when startup is finished.
-  content::BrowserThread::PostAfterStartupTask(
+  // Use BEST_EFFORT as those will only run after startup is finished.
+  content::BrowserThread::PostBestEffortTask(
       FROM_HERE, base::SequencedTaskRunnerHandle::Get(),
       base::BindOnce(&ModuleInspector::OnStartupFinished,
                      weak_ptr_factory_.GetWeakPtr()));