DPWA: migrate RunOnOsLoginCommand to use AppLock

Migrate to access web app resources through `AppLock`.

Bug: 1375870
Change-Id: I9ea4625239df5c7fc76bdfb8205eee5a7f43c885
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4026910


Auto-Submit: Phillis Tang <phillis@chromium.org>
Reviewed-by: Daniel Murphy <dmurph@chromium.org>
Commit-Queue: Nancy Wang <nancylingwang@chromium.org>
Reviewed-by: Dibyajyoti Pal <dibyapal@chromium.org>
Reviewed-by: Nancy Wang <nancylingwang@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1071923}