settings: Sync all throughout oobe for device settings

Previously there was a race condition between device settings syncing
and a keyboard/mouse/touchpad being recognized. During oobe, assume that
any change in settings should update the connected devices as well as
this is when sync is done and sync may happen after a keyboard is connected.

Bug: b/345510722
Change-Id: I523f9b227e2bbec97c5adc3099a242f63b49061b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5595109
Commit-Queue: David Padlipsky <dpad@google.com>
Reviewed-by: Jimmy Gong <jimmyxgong@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1311494}