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This CL also moved click tracking into QuickAnswersClient to reduce code
duplication and make all logging handled by QuickAnswersClient.

Bug: 1060265
Test: manual test
Change-Id: Ia3ae5d0101a8096aa745c7a797be504bc4093025
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2096927
Commit-Queue: Li Lin <llin@chromium.org>
Reviewed-by: Xiyuan Xia <xiyuan@chromium.org>
Reviewed-by: Avi Drissman <avi@chromium.org>
Cr-Commit-Position: refs/heads/master@{#748910}