AutoSignOut: Add guards before instantiating AutoSignOutService

- Adds profile checking before creating the service as
the keyed services that are needed (e.g. DeviceInfoSyncService) work
with regular profiles only and not `OffTheRecord` profiles.

- Adds a Sync flag check to avoid breaking tests that have Sync
disabled since it needs to be enabled for AutoSignOutService.

Bug: b:433240810
Change-Id: I744268b0040c92c6a8e08da62cf51adbc27fee1b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6955088
Commit-Queue: Omar Bahgat <omarbahgat@google.com>
Reviewed-by: Andrey Davydov <andreydav@google.com>
Reviewed-by: Hidehiko Abe <hidehiko@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1520593}