How can I assign a background app to “All desktops” (using Spaces)

I use the Spaces feature to have multiple desktops and want to assign a background app to “All Desktops”. Because background apps don’t have dock icons, I can’t use the normal method of right-clicking the Dock icon and choosing Options > All Desktops. The app I want to do this with at the moment is the Carbon Copy Cloner Task Progress window, but there have been others in the past. One thought I had is that maybe I could do this with AppleScript, but I haven’t been able to figure out how or if it’s definitively not possible. Does anyone on the forum know? I realise it’s likely not possible but thought I’d check in case I’m missing something. Thanks!