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The type logically belongs to the notification handler itself,
so move it there. (NotificationCommon will hopefully go away
entirely not too long from now.)

In addition, rename PERSISTENT and NON_PERSISTENT to WEB_*
to clarify the fact that these are Web Notifications. We'll
continue to follow the spec for the persistent/non-persistent
part, that's now reasonably consistent throughout our code too.

TBR=stevenjb@ for //c/b/chromeos, dtrainor@ for //c/b/download
BUG=

Change-Id: I1a5ccf7ee63949a258da301455a84b3cceeca53d
Reviewed-on: https://chromium-review.googlesource.com/741719
Commit-Queue: Peter Beverloo <peter@chromium.org>
Reviewed-by: David Trainor <dtrainor@chromium.org>
Reviewed-by: Peter Beverloo <peter@chromium.org>
Reviewed-by: Steven Bennetts <stevenjb@chromium.org>
Reviewed-by: Evan Stade <estade@chromium.org>
Cr-Commit-Position: refs/heads/master@{#518973}