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As suggested in recent reviews, it's desirable to keep the sync-related
source code in a dedicated directory, with separate OWNERS file. The
files still belong to the same build targets, because there would be
cyclic build dependencies otherwise.

While moving the files, various trivial changes are introduced to avoid
presubmit and linter errors.

Bug: None
Cq-Include-Trybots: luci.chromium.try:ios-simulator-cronet;luci.chromium.try:ios-simulator-full-configs
Change-Id: I8ce0070e2449f4285c3ccaa85e9d550d61433744
Reviewed-on: https://chromium-review.googlesource.com/1256809Reviewed-by: Scott Violet <sky@chromium.org>
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/master@{#595892}