Inform user about unclean shutdowns

### Description

The recent bug #6827 showed that watchdog can cause system reboots. In general, its hard to tell for users when a system reboots unexpectedly. We could write a marker file which we delete on clean shutdown to detect unclean shutdowns, and inform the user about it.

Maybe it is also possible to detect if watchdog caused a reboot. If so, we should definitely include this information as well.

The recorder in Core already has a similar feature. But from what I am aware it only surfaces as a warning in the Core logs currently.

### Additional context

_No response_

No implementation files or tests are named. Start by reviewing issue #6827 and the recorder's existing Core behavior; identify where Supervisor can persist and remove a shutdown marker. Done means users are informed about unclean reboots, with watchdog attribution included if it can be detected.

Written by the indexing model from the issue text.