Can you give us a shot of the space straight on so we can see more of the wall to the left?

I would be inclined to close up the opening under the bottom flight of stairs, then find or build something that goes with what looks to be an industrial vibe.

Vintage French Factory Bar Cart · More Info

I say build because it might be nice to have a cabinet that follows the angle of the second flight of stairs.

following

Because the stairs are open I would not enclose the area under them. Dust will get inside there and settle and there will be no way to clean it. The beauty of an open staircase like that is in the fact that it is open. Is this space already built? Is there any changing some things? A bathroom across from a pantry is an odd configuration. What is the counter between the bathroom and the pantry? That seams more like a bar area? What about the area near the slider but to the left of the stairs? that area seams like a more ideal area for what you're describing than under the stairs.

If you do a google image search for “wine cellar under floating stairs” lots of ideas come up to make use of the space while maintaining the open feel.

Dr rv

The stairs are interesting, and sculptural. Anything else you do will limit the effect you have now.
I'd not build anything under them.

My bad. I just realized the stairs were open. In which case, putting a cabinet there will ruin the effect. You can do this:

Anything you put under there will get dusty from traffic up and down the stairs (dirt falling off shoes, etc.), so be sure you can close whatever you put there. I have a very dark bookcase next to my open stairs and there's always schmutz on it.

Some inspiration