Add back Profile reference from web_contents_state.cc

Not a clean revert as other dependent CLs over this. The code is a clean
revert, but the build target that was split out in
https://chromium-review.googlesource.com/c/chromium/src/+/2246983 is
merged back into //chrome/browser.

Also leave Profile#setLastUsedProfileForTesting() which has been
used by many tests since then.

Reason for revert: crbug.com/1108345

Original change's description:
> Remove Profile reference from web_contents_state.cc
>
> Bug: 1090048
> Change-Id: I156fa5e8b6258d453c5809247e809a4ec7957125
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2281307
> Reviewed-by: David Trainor <dtrainor@chromium.org>
> Commit-Queue: Henrique Nakashima <hnakashima@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#787271}

Bug: 1090048
Change-Id: Iab4e650ed3fe9a559e58ea7462fad5199999ee74
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2324105
Reviewed-by: David Trainor <dtrainor@chromium.org>
Commit-Queue: Henrique Nakashima <hnakashima@chromium.org>
Cr-Commit-Position: refs/heads/master@{#793430}