[NTPFooter] Add browser->WebUI interface

This allows passing messages for management notice text and logo changes
as well as extension attribution changes.

We also pass the WebContents to the handler which will be used for the
management notice in follow-up CL.

Note: this CL does not introduce any new UI or change the current footer
behavior.

Bug: 414583889
Change-Id: Ie4cb10c6b8864f2c2289de4a5f6fe9bb2c845345
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6497419
Reviewed-by: Joe Mason <joenotcharles@google.com>
Commit-Queue: Salma Elmahallawy <esalma@google.com>
Reviewed-by: Paul Adedeji <pauladedeji@google.com>
Cr-Commit-Position: refs/heads/main@{#1455981}