I've designed this kitchen utensil rod based on a clothes hanger design. For the rod, I've used an aluminium corner profile with a width of 11.5 mm.

To install, stick two-sided duct tape between the walls and the rod to increase friction, then unscrew the nut until the rod is fixed in place. I would recommend tightening the nut after a few days when the plastic deforms under pressure a bit.