Window ledge needs nothing. It’s too narrow for any display. However, the bare wall to left of window seems to be crying for something! Do you have some large, nature inspired art to hang there? Could be a wrapped canvas or a metal work art of trees /leaf etc. Is that another window I see a bit of through the higher railing on right? If it is & you plan to have a window treatment / shade on it, I’d duplicate the same treatment for the window in the stair well that you’re asking about. Also, plantation shutters are lovely but they do cover much of a window with their frames. IMO, they’re maybe too bulky & heavy looking for that window.

Plantation shutters seem to bulky and hefy for this space. I'd add decoration to the left of the window to bring your attention there instead of focusing on the window. No decoration need on the ledge. It is narrow and just not meant for display.

This staircase already has a lot of visual information - turns, spindles, lots of levels to your newel posts, and wood contrasting the white everywhere. Simplify, simplify, simplify. No window dressing. Nothing on the wall to the left of the window. Decorate the wall that is at a 90-degree angle to the left of this window wall.

Nope, the window ledge doesn't need anything!

Skyscape next to the window since your window film deprives you of the sky and outdoors.

I agree that you need art on the wall to take your focus from the plain glass.

No need for anything on ledge! It's thin narrow. Large art on wall. If no one see end, window bare. If need a remote blind.

You can commission an artist to build you a stained glass window insert. It fits inside the current window. There may be ready made stained glass windows that will fit when used with a wood frame.

Apple pie order has a brilliant idea!
Stained glass will enhance that window in a most pleasant illuminating way.
Any coverings like shutters will need dusting and swabbing,so why add extra chores.
Some art piece at left side would also add visual appeal.

“You can commission an artist to build you a stained glass window insert.” This is a good idea & one that we did in a home for a very large window high up in the entry over front door. Our issue was that at night with interior lights on, a person could be seen from outside & house across the street when standing, walking across large open landing at top of stairs - where all the bedrooms were. The window we had made wasn’t ’stained’ glass but was leaded glass with the glass being obscured & with a design created in the window by the gold / brass color lead pieces holding the design together. Light came through the window but the visual was completely obscured. This glass was mounted into the window frame with something like wall mirror holders. We did have our window professionally installed because it required 2 people on ladders for an interior & essentially a 2nd floor window without a 2nd floor. Beyond our DIY skills.

Georgia O'Keefe's "Ladder to the Moon" is a beautiful image you can get as a poster in multiple sizes from multiple online sources. It would look beautiful at the top of your staircase.

An interesting outside mounted blind can be pulled down just past the ledge, which fixes that. It also will look more finished.