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Adds the last_updated_timestamp field to DeviceInfo and populate it with
the already existing field of the same name in the sync proto.

Use that value instead of using the change processor in the
SendTabToSelfBridge.

Bug: 959487
Change-Id: If84605055988c2d5deb4f5f0be373cc7d4368f0f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1598550
Commit-Queue: sebsg <sebsg@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Reviewed-by: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/master@{#658298}