I agree with finding a finish carpenter to quote you some doors.
INCLUDING: bifold doors.
(it looks as though it was made for a single bifold door, actually)
And just leave the space in front open; don't put anything in there. You need to stand there to get stuff out of the closet, and if the door is a bifold door, you need room for it to move. And the wall behind you will keep you from falling down the stairs.
At the most, maybe a thin decorative thing--a column with silk flowers on the top, or something. I think I'd want it low down, but some might like it sticking up over the railing.
Or, a small stool (maybe a vintage/antique piano stool?)
Q