Get a atircase company to give you some clue as to the cost .. Staircase remodels are expensive and if not modern opening this might not be what works for you. The company can aslo advise on the best style .

I'd tolerate a bit of mess to see what you are working with, and hire a builder to remove the sheetrock and see what is behind it. Support, no doubt, but other utilities hidden.

The worst case, you would need to re sheetrock the stairway and trim it out and paint it back to original. For me, worth it, but a personal choice.

Photos of everything exposed in the search, to show a stairway professional for a new look.

I think it would look great! Obviously as others have said first figure out what may be inside those walls , then come up with the plan.

Good luck! Be sure to post after pictures

I actually think what you have is a pretty clean resolution visually, especially since there is a table right against it. With all that removed you will be looking at a forest of spindles and furniture legs. Unless you did a completely floating mono-stringer staircase with a glass handrail or mesh or something.

I think it would look great, too. I'd remove the drywall from the first floor up and then replace it with balusters and a handrail. Anything below the first floor to the basement, I'd leave as is. I happen to like the look of balusters rather than drywall--it feels more open and less closed in.

Spending 100K on the stairs as a whole is not going to make 100K worth of difference. And zero expenditure will do anything to move the needle on home value. So you have to figure out the maximum that you would be willing to spend on this, just for your own pleasure. For sure your own pleasure, as no buyer is going to find something so visually intrusive to be as attractive as it is now. It doesn't need to be the 100K of open stringer with glass panels to be unobtrusive. Sometimes a bit of wall gives us just that.

Seems like the walls could be demoed DIY and not cost much at all. Do you know that the walls are structural at all?

I think it looks fine.

Not sure the money spent will provide much of a change in this space.

Looked for some Houzz photos ... but most are in larger rooms/homes and don't have basement stairs to complicate things. Only this one came close.

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I would make sure before I did anything that the rise over run you have is still compliant. Many of the houses in my area that have these crossways stairs dividing space in a house, they are too steep/short to meet modern requirements. I have live in two places with this condition. Most people do not touch the stairs, even with other extensive renovations because of this, they leave them in their grandfathered existing condition.

I've seen open staircases in townhouses with similar layouts, but yours looks better as is.

As others have noted it might open up a can of worms if you decide to change the stairs.

I like it how it is, clean and unobtrusive - not everything should be a feature

I personally would wall the whole thing off. As it is now, it intrudes and provides no nice view of the opposite spaces. It might be that you would need a soffit to accommodate the height of the staircase. To me that would provide a natural break between the living/dining room and the kitchen. Hire an architect or designer with a vision.