You're thinking wire shelves?
I don't know if they do come very deep. I see them at 24"

Whoops--I'm wrong--there are some at 36" deep
These guys have some--I don't know what configurations (like, if it's a bookcase worth, or whether you can buy just a shelf to cut down)
https://www.theshelvingstore.com/
shelving.com

But you could have shelves made of wood that have radiator grill panels in them. Basically, wooden shelves with a section cut out and replaced with that perforated metal panel that they use in radiator covers.

One thing this solution would let you do is, you could have the back part of the shelves be solid, and only the front part (where the towels would be) be cut out to hold this.

Most carpenter folks could make it--they might need to route out a lip around the cut-out section.

It's usually paintable.

There's also the idea of making the shelves out of slats of wood that are spaced a bit apart (sort of like bed slats). If you install side cleats on the wall of the closet, then you can just lay the strips of wood on the cleats and tack them in place (with a nail gun or even just a simple finishing nail).
Or, you can lay out the slats and then attach a cross piece going across on both sides (or the very ends) to make a rigid shape. (flip it over so the cross pieces are on the underside). Like a palette, sort of.

Or, making solid wood (or plywood, or MDF, or melamine-over-particlewood) shelves and then using a small hole saw or a spade bit to drill holes in them all over the place, focusing on the middle where the towels would be. Time consuming, but simple. (if you DIY this, place the shelf on a piece of sacrificial lumber when you're drilling, to prevent blowout in the back)

Using the back of the shelves for long-term storage is a great idea! You'll find that when your shelves are effectively half as deep, they are much easier to keep organized.