I just built a stand with those exact type of doors, got some neodymium magnets off amazon and a forstner wood bit to inset them in the wood, cemented them in and they work great, I painted over them and you can’t hardly see them
Ive done them by supergluing the magnet to the removable door or stand and on the other side using a washer so when I place the door the recession is perfect. Now you can recess the magnet if needed to get the look your looking for.
I am recessing the magnets in the panels with epoxy. Stand is steel so I will not have to do anything there. I printed brakets to support the weight so all the magnets have to do is hold them on.