[omnibox chrome:omnibox] Connect the browser's omnibox, CL 1 of 2

Interacting with the real omnibox of any normal or incognito browser window
while the debug page is open will update the debug page's output.

This is the 1st of 2 related CL's. This CL wires in the browser omnibox,
whereas the 2nd will add a UI input to disable this feature.

Bug: 891303
Change-Id: I64d72ed01710d4eb472373527f7ade61c19b0fda
Reviewed-on: https://chromium-review.googlesource.com/c/1399450
Reviewed-by: Jochen Eisinger <jochen@chromium.org>
Reviewed-by: Dominick Ng <dominickn@chromium.org>
Reviewed-by: Tommy Li <tommycli@chromium.org>
Commit-Queue: manuk hovanesian <manukh@chromium.org>
Cr-Commit-Position: refs/heads/master@{#622476}
13 files changed