Getting that all uniform is a job for a master plasterer. I've been doing remodeling work for decades and that is not a job I would tackle myself if I wanted it to look decent. I suspect the wallpaper was on it as it was a simpler way to disguise the variations in the surface.

You can buy paintable wallpaper, with a texture, or even a design texture, at the big box stores, and then just paint over the top of it. Probably the easiest. May take two people to put it up though.

Do you have a better photo? What do you mean by “spirals around”?

I don't understand 'spirals around' either beyond what I can see in the photo.

Is this an intentional design feature? Or just really, really bad interior finishing?

I presume the OP is referring to the underside of a spiral staircase. The photo is not very helpful, but I thought it was plaster with exposed lath.

Why don’t you just leave it? It has a beautiful patina and is so unusual — I think you should display it as a historic artifact. It would be lovely to decorate around especially in the basement of a 100 year old house. If all the walls and ceiling are white, this will stand out tremendously! Please don’t cover it.