Spectrwm(rather obscure, but I like it) has a free window mode for things like this. where free windows are in all workspaces. Define some hotkeys for the special app invocation and perhaps add a protected region to keep normal windows out.

https://github.com/conformal/spectrwm

And a rendered manual https://manpages.debian.org/trixie/spectrwm/spectrwm.1.en.ht...

I had fun figuring it out one day, but the way I use the computer it did not provide much utility. so my config stays rather stock.