On Linux, you can try Xephyr (https://www.freedesktop.org/wiki/Software/Xephyr/, https://wiki.archlinux.org/title/Xephyr). It's not as nice as DeskPad, but you can basically achieve the same thing.

It's too easy to just use OBS for this, in my opinion. Add the pipewire display capture, add a filter to crop it to a corner, stretch that container to fit the stage, open the window in the corner. Fairly simple.