GitLab

The class is only used under sync/engine_impl and in fact shouldn't be
used outside, so let's move it away from base/.

While moving it, a few minor things are refactored, such as a few
functions being renamed for clarity.

Change-Id: Ibaf6e662551eeb78e2b7c7cbc88778b54cf31ee2
Bug: 1129782
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2484697Reviewed-by: Marc Treib <treib@chromium.org>
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/master@{#818459}