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This CL removes unneeded public API from the BVC, primarily the public
dispatcher property. The NTP perf test and the BVC unit tests were the
remaining places where these dependencies were used.

In addition to the command dispatcher, the public TabModel and
BrowserState properties of the BVC are removed. Some other properties
(FullscreenController, TypingShield) are just moved internally.

The ContentArea property was only used in the BVC unit test, and only
to check that the BVC was attached to the containing view controller.
Since the container is provided to the BVC as well, that can be tested
without using any direct BVC API.

Other minor cleanup:

 - Some BVC includes are pruned.
 - Internally, the protocols that the dispatcher conforms to are
   reduced in number.
 - The internal -shieldWasTapped: method was removed, since
   it just forwarded to the dispatcher.

Change-Id: I2f0ae3382e32867e5aad7a083b8fcbbb384b5c53
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2135620
Commit-Queue: Mark Cogan <marq@chromium.org>
Reviewed-by: Stepan Khapugin <stkhapugin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#757034}