[scheduler] Migrating chrome/browser/ to PostTask.runOrPostTask.

Bug: 863341
Change-Id: I593f394db9984021772191cc713928f662ed9987
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1494886
Commit-Queue: Karolina Soltys <ksolt@chromium.org>
Reviewed-by: Andrew Grieve <agrieve@chromium.org>
Reviewed-by: Sami Kyöstilä <skyostil@chromium.org>
Cr-Commit-Position: refs/heads/master@{#641849}
22 files changed