I recently purchased the Display HAT Mini for my Pi 5, and am looking for an external enclosure. I have it connected via ribbon cable. I already have a relay board connected directly to the Pi, so the display needs to be external. Unless someone can suggest a case that would accommodate both and allow the display to be viewed from the top.
There are a few around on the 3D printing websites, although I’m not sure if there are any which would suit your needs. That’s the route I had to go down when I put my display together, but my case won’t work for you as I’m running from a Pi Zero.
Either that or design your own and have it 3D printed, although that of course is a lot of work.
There aren’t really any commercially available cases built to accomodate the DHM.