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This CL updates BadgeMediator to be constructed with a Browser in
preparation for a follow-up CL where the mediator will observe the
OverlayPresenter for the Browser in order to update the
InfobarBadgeTabHelper for banner presentations and dismissals.

This CL also cleans up and updates the mediator:
- Adds readwrite property for the active WebState, allowing easy
  access to the WebState as well as facilitating idempotent updates
  via |-updateForNewWebState:oldWebState:|.
- Adds a readonly property for the active WebState's
  InfobarBadgeTabHelper.
- Since a Browser's BrowserState is constant over the Browser's
  lifetime, we don't need to check whether the newly-activated
  WebState is incognito.  Instead, the incognito badge item is just
  created once upon initialization.
- Updates order of protocol implementations to match declaration
  order.
- Updates test fixture to use params so that both the incognito and
  normal browsing behavior can be tested.

Bug: 1030357
Change-Id: If7a5b4761ea4fd8e558120d1cfc14eb806c75290
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1986860
Commit-Queue: Kurt Horimoto <kkhorimoto@chromium.org>
Reviewed-by: Eugene But <eugenebut@chromium.org>
Reviewed-by: Chris Lu <thegreenfrog@chromium.org>
Cr-Commit-Position: refs/heads/master@{#728740}