Is this solution different from just executing this:

    docker run -it --rm -e DISPLAY --net=host -v $XAUTHORITY:/root/.Xauthority -v /tmp/.X11-unix:/tmp/.X11-unix debian:12-slim

And then run the GUI app in the container? For example for Firefox:

    apt update
    apt install firefox-esr
    firefox

That is an approach I sometimes use to try GUI applications in a Docker container.