[PWA] Add/remove kUserInstalled source as needed

This changes makes sure that apps get the kUserInstalled source
when they are user installed, as well as making sure that the kSync
source is only added if sync is enabled at the time. This CL
also adds logic to remove the kSync install source when sync is
disabled, leaving just kUserInstalled.

All of this is guarded behind the kWebAppDontAddExistingAppsToSync
feature, and tests (other than WebAppIntegration tests) have been
updated to work with and without the feature enabled. Integration
tests will be added/updated in a follow-up CL.

Bug: 371033179
Change-Id: If70ef30dfc707549f802b37e51d04933becfb247
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5905960
Reviewed-by: Daniel Murphy <dmurph@chromium.org>
Commit-Queue: Marijn Kruisselbrink <mek@chromium.org>
Auto-Submit: Marijn Kruisselbrink <mek@chromium.org>
Reviewed-by: Brett Wilson <brettw@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1366465}