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If the user starts chrome by launching the WebApp that is being migrated
from, then Chrome crashed due to shutting down while the browser object
is still being used by the migration code. This patch ensures that the
browser doesn't exit during migration, and only keeps the browser alive
during the migration itself.

Note: This WebAppMover is not a permanent class, and will be removed
after the Chat app is successfully migrated.

Design Doc (Googlers only):
https://docs.google.com/document/d/1GOek_Q4O_jTewHHx0MLnbYXvlTdEKT-KmkPZ5R0VJ3c/edit?resourcekey=0-K35fuzesohP36-qKSGbp0g

Bug: 1165603
Change-Id: I3a38402513e3dacdd05b5d516b01f371043d5206
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2622584
Commit-Queue: Daniel Murphy <dmurph@chromium.org>
Reviewed-by: Colin Blundell <blundell@chromium.org>
Reviewed-by: Chase Phillips <cmp@chromium.org>
Auto-Submit: Daniel Murphy <dmurph@chromium.org>
Cr-Commit-Position: refs/heads/master@{#843680}