[PushMessaging] Rename PushMessagingAppIdentifier to push_messaging::AppIdentifier

This is a prerequisite of moving PushMessagingAppIdentifier to the
//components in https://crrev.com/c/6892103. It renames
PushMessagingAppIdentifier to push_messaging::AppIdentifier, so that the
following move will be much smaller without the boilerplate renaming
changes.

After this CL, another CL will change PersistToPrefs and DeleteFromPrefs
to be the static functions which avoids push_messaging::AppIdentifier
from depending on the Profile.

Some of the changes here will be reverted later, e.g.
PushMessagingAppIdentifier::RegisterProfilePrefs, after the split of
push_messaging::AppIdentifier and
//chrome/browser/push_messaging/push_messaging_app_identifier.

Bug: 440400313
Change-Id: Ic6d1580187288d6126b1fec75855cdeb0b56708b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6912514
Commit-Queue: Zijie He <zijiehe@google.com>
Reviewed-by: Peter Beverloo <peter@chromium.org>
Reviewed-by: Lei Zhang <thestig@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1512616}