Also not a pro but I agree with njmomma. Try to incorporate some extra storage. You don't want to put decorative items up there as they will just be dust catchers.

Just brainstorming, but I'm thinking storage cabinets with fronts that look like window frames. You could use a speckled glass or mirrors instead of window glass and it would look like you had a row of clerestory windows.

Dry wall and forget no way are you going climb up and down to use it as storage

I'd align several lidded baskets and use them to store off-season clothing and shoes.

Something like this, maybe...

Rattan Rectangular Lidded Storage Basket · More Info

I hate say this, but it is not a good space for storage. I would drywall it and forget it. The way it is now it is a huge dust collector.

Ditch the cardboard file box, buy a telescoping duster, and stop staring at it. The trim/drywall $$$will be more than you think, when done correctly.......and you don't need it for occasional storage that badly, or you'd have done it.

Have a glass company cut a mirror for the back wall to fit...........bye, drywall. It will feel like an extension of the closet. Couple hundred bucks MAX. Buy one nice sculptural 'THING" . When you find it. Perfect shape below for the space. Call the thing done and great looking for 700 bucks, 500 of which can go on a move if that happens.. Or do what most do ? Get some fluffy faux green plant thing. Please don't : )

https://www.perigold.com/decor/hd0/goddess-of-the-sea-sculpture-l1191-k~gxv4491.html?refid=GX203202969287-GXV4491&device=c&ptid=383563671734&network=g&targetid=pla-383563671734&gclid=EAIaIQobChMIrK6RuuDA3QIVw0oNCh1xbg2BEAQYBCABEgLWMPD_BwE

Thank you all, I like the idea of a trunk or storage boxes. The idea with the windows also sounds very interesting