How do I turn my closet into an office?

https://www.familyhandyman.com/home-office/how-to-turn-a-closet-into-an-office/view-all/

A lot depends on what kind of function you need. Make a list of tasks you intend to do in the space. What do you need to accomplish them? Do you need space for a laptop? How much paper will you be handling? If you need to file a lot of paper, you might want to make a desk with a two-drawer filing cabinet under one end and attach the other end to the wall. Basically, once you know what you need to function, start with that, and the cute will follow! Have fun with this!

I would make it over with wood shelving using your rail system, and a larger wooden desk top out of birch veneer plywood and use wooden iron-on trim on the edges. If you have cords coming up from the floor to say a computer, you can use a hole saw to make a hole in the desk top near a back corner. Stain it or just finish it.

I might just paint the walls a bright happy color.

That is a small space. If you want to keep the rail system, here's what I would do. Take out the bins. Get a 2' wooden shelf to use as a desk. Put narrower glass shelves on top to give the illusion of depth. Keep everything as simple and clutter-free as possible. Use pretty boxes to hide things such as stapler, tape dispenser, etc. Get a gorgeous cup for scissors and writing instruments. Put a framed picture or quote on each side wall.

Good ideas above. I have done this with my computer. Used a piece of wood for desk top after removing metal shelves as in pic. Left uppers and used cute magazine holders for magazines, paper, mailing supplies. Also added a piece of foam board covered with wrapping paper for pin ups like notes, pics, reminders, etc.