I can’t think of a straightforward way to dynamically adjust the background today. Maybe the community has ideas though?
I suspect that the Variables in Media Tiles feature request would be a good starting point for this if you want to cast a vote there. Once that’s in place, the same logic could likely be used in Dashboard Backgrounds. Then the last thing that would be needed would be some sort of JSON Parsing in Rules to be able to get just the part you need and put it into a variable.