Why not come up with a custom Whonix specific background similar to this:
or this:
with the Whonix logo and then maybe in the bottom right corner something like “Whonix Workstation persistent” and respectivley for live mode and the gateway.
Checking if we run live or on the gateway or workstation is not the problem. I’ll take a closer look at the other points.
If we can check if the current wallpaper uses another image than the one we officially would use we could prevent changing it back in case the user has set a custom one. Maybe a similar check could be made e.g. check if we run on 13 and just don’t install the package. However, this would also mean you can’t easily distinguish between live and persistent mode. During some (or all?) of my tests upgrading 13 to 14 the background changed anyways. As far as I can remember also during some normal non-whonix upgrades between debian versions. So it is something which could be expected.