Update `web_app_install_finalizer` with a clock so tests can use a mocked clock.

Currently, the tests are using `base::Time::Now()` which causes flaky
results in tests.

Bug: 413277594
Change-Id: If03a5d35331056aa541c653a245fe4426390160c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6495218
Commit-Queue: Daniel Murphy <dmurph@chromium.org>
Auto-Submit: Daniel Murphy <dmurph@chromium.org>
Reviewed-by: Dibyajyoti Pal <dibyapal@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1452880}