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This CL removes any code in favicon_cache that related to favicon sync
or that is not needed by the only remaining purpose of the class.

This CL does not change behavior w.r.t. the remaining public API.

Removing the class completely is left for follow-ups.

Bug: 978775
Change-Id: Ibb69eb0258a78f056d762bf01b27a94b638a04d0
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2144137
Auto-Submit: Jan Krcal <jkrcal@chromium.org>
Reviewed-by: Mikel Astiz <mastiz@chromium.org>
Commit-Queue: Jan Krcal <jkrcal@chromium.org>
Cr-Commit-Position: refs/heads/master@{#760025}