These little ledges are such a pain, I feel you. Honestly, I wouldn't bother putting anything up there. It will collect dust regardless unless you box it up, but at least it will be easier to clean without a ton of small items (or fake plants) up there.

First choice, have it drywalled flush with the rest of the wall(s) -- this seems absolute best from a dust allergy point of view. Second choice, 1-3 interesting sculptural items on the LR-facing side -- could be a neat piece of driftwood, or a small scuplture and a vase... Third choice, leave it blank, "architectural interest" or cat jungle gym.

Some ideas -

You can make the thermostat disappear behind a tall table lamp that does not generate heat or amongst a grouping of pictures/mirrors or both.

I like the cove molding in image 3

And you can take the ledge to the ceiling with the treatment in image 4

My first choice would be to have it drywalled over, that shelf is a horrible dust collector even without objects on it. Barring that option I would just ignore it , leave it blank until I wanted to ( or could ) have it drywalled.

make a cat ladder ..they love hights

I can’t see the point of that wall where the ledge is it looks like it could just be removed all those arches would make me crazy