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This CLs organizes most of the drag and drop logic to its own
manager service, in preparation for more complex logic. This CL
does not change any implementation and only moves code around.

Follow up CLs will modify the drag interactions to only modify the
DOM and allow canceling drag sessions, with drop being the commit
to move tabs or tab groups. This will also prepare the manager to
be able to support dragging tabs from other windows into place.

Bug: 1048894
Change-Id: Ieb66ee859a09b972f178a8c50513aa2f284e08d6
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2036932Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
Commit-Queue: John Lee <johntlee@chromium.org>
Cr-Commit-Position: refs/heads/master@{#738668}