I an attempt to get away from using 3/4″ playwood on everything, I designed the new bar back using 1/2″ plywood.
Since the computer CAD design process does not model loading & gravity (easily) I figure that 3/4″ plywood may be a better choice if you want to heavily load the shelves.
You would have to adjust the trim dimensions accordingly since the thicker material would throw these measurements off by 1/8″ on each side (1/4″ total).
The design should be just fine, since adding the finish side panels makes the side 3/4″ thick. and the long span above the mirror is actually 1 full inch thick when you add the overhead glass rack.
If not 3/4″, then maybe 5/8″ would be better for making it a bit more heavy duty.
Just something to think about…