Is there room to the right for a barn door that would slide over the opening at the bottom of the stairs?

Is there no guard rail at the upper floor?

I've seen the upper part enclosed with glass. A door is allowed at the top riser if it doesn't swing over the stair.

Is there enough room for a landing at the top of the stairs for a wall (the RED line) - of course would require eliminating the open rail. Or room to enclose a wall on the BLUE line keeping a "loft" open landing?

I just updated the pictures to try and answer the last few questions. I’m afraid adding a wall in either of those spaces would really take away from the openness/light of the room. I’ll definitely consider it though.

I don't know, I thought the purpose of doors is to take away openness. I guess you have to decide whether privacy is a priority. Sure looks to me like plenty of light, a window in the stairwell, a window in the bedroom. Room for a door swing at the blue line and still have a small "loft."

This is a very good idea as well!

Curtains and blinds don't keep the kids or pizza delivery guy from barging in.

Here's another recent thread that has suggestions

www.houzz.com/discussions/6075749/how-to-add-a-soundproof-door-to-bottom-of-this-awkward-staircase

Those winders are way out of code anyway; you've got at least a 14" riser at the apex, probably 21". A little step at French doors at the bottom seems quaint comparatively speaking.

Play some really loud music.