>>889594There's no fucking reason to have some nasty ass 2x4s going all the way to the fucking floor.
OP. Get out the stud finder and mark out all your studs. Get a length of 1x3 and paint it to match the walls or stain it if its a nice wood.
Cut a length for the back wall. Position it so the top of the slat is 1-2 inches over the rod. Use a level to ensure its flat. Pre drill the wood, countersink, and use 1-3/4" countersink screws to attach the cleat into the center of the studs it crosses over.
Measure for the length of the side slats. Make the cut that butts up to the slat on the back wall at a slight angle so that the slight knife edge can be pressed firmly into the back slat for a tight joint for appearences. Again screw into the studs.
Cut a piece of veneer plywood to fit. half inch is fine, but 3/4 for more "project done right" points. Secure the shelf with two screws down into the back cleat. Face the plywood with a strip of edge banding before securing it in place for a finished look.
Two screws for each stud to secure the cleats in that size closet and you could load hundreds of pounds on the shelf before the shelf itself gives way with no crossbeam support underneath. I have a shelf made like this in my garage with the cleats holding about a thousand pounds and no sign of fatigue