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This CL adds a feature to sync the DnD status between Chrome and Android.
- When the DnD status is changed on Android side, set it to Chrome-side.
- When the DnD status is changed on Chrome side, set it to Android-side.

Bug: b/79951342
Test: Ran added tests
Change-Id: I3eba63420a91de60e7baf333dfb4dd7c1da74310
Reviewed-on: https://chromium-review.googlesource.com/1111495
Commit-Queue: Yoshiki Iguchi <yoshiki@chromium.org>
Reviewed-by: Yusuke Sato <yusukes@chromium.org>
Reviewed-by: Greg Kerr <kerrnel@chromium.org>
Reviewed-by: Eliot Courtney <edcourtney@chromium.org>
Cr-Commit-Position: refs/heads/master@{#570357}