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The tab search feature will only support a fixed entry point in the
tab strip region view going forward. This change removes the
implementation of the tab search button that sits flush with the new
tab button in the tab strip.

This reverts most of the changes introduced in the following CLs:
https://crrev.com/c/2333341
https://crrev.com/c/2377550

Bug: 1099917
Change-Id: I4013e3724968374b8616550c54d562da1366d0af
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2487252
Commit-Queue: Thomas Lukaszewicz <tluk@chromium.org>
Reviewed-by: Scott Violet <sky@chromium.org>
Cr-Commit-Position: refs/heads/master@{#819136}