GitLab

Update the echoPrivate API to use the new task scheduling API, as well
as the dedicated Extensions-related file task runner.

Bug: 689520
Bug: 750122
Change-Id: Ie6d403cb700c71bc9faabd828b2f40f0826f85bd
Reviewed-on: https://chromium-review.googlesource.com/598464
Commit-Queue: Devlin <rdevlin.cronin@chromium.org>
Reviewed-by: Karan Bhatia <karandeepb@chromium.org>
Cr-Commit-Position: refs/heads/master@{#491515}