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WebUI has access to the Browser, so this should allow interfacing with Mohnstrudel. It also allows us to clean up a good portion of TabStripController that was only being used by the Editor Bubble.

Still left to do: make it so that the dialog doesn't necesesarily need to take a TabGroupHeader.

Bug: 1055537
Change-Id: Ia341453a092a8083075d7a31b6e39705d883fbfc
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2072365
Commit-Queue: Connie Wan <connily@chromium.org>
Reviewed-by: Charlene Yan <cyan@chromium.org>
Cr-Commit-Position: refs/heads/master@{#745309}