[dPWA] Migrating uses of deprecated registrar to registrar_unsafe

This CL is migrating usage of WebAppProvider::registrar to
WebAppProvider::registrar_unsafe before WebAppProvider::registrar
is removed.

Design doc linked in crbug.com/1399641

There is no functional change in this CL.

This CL was uploaded by git cl split.

R=ortuno@chromium.org

Bug: 1399641 b/260863363
Change-Id: I126e76b33a74936a1e77badd11e79ee46b9b3edd
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4087865
Auto-Submit: Camden King <camdenking@google.com>
Reviewed-by: Jiewei Qian <qjw@chromium.org>
Commit-Queue: Jiewei Qian <qjw@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1082315}