Picture added!!

Paint it all a smoke/charcoal grey then use a high contract wall paper in triangle areas like white and charcoal damask

You might consider keeping the handrail and the stair treads the wood tone, and painting out the rest in white. A trick for the walls might be to use gradually lightening paint on each as you go up, to give an impression of more light. See Houzz Photos under "stairway" for more options, such as wainscoting, niches, or wood trim.

Although I just noticed your floors. IDK that I would go with the greys. I know everyone is hoping on this grey train but it will fade. Your floors are nice and the colors are a nice contrast. Change the railings and add a nice wall paper.

Instead of grey handrails, I think black would create some contrast (already have a lot of grey) and white spindles will be really nice. It took me over 35 hours to do ours (3 levels), but well worth it. Perhaps if you waited until the staircase was completed, you may feel you don't have to add anything to the walls, especially once you add artwork upstairs and on wall to the right.

Dark grey handrails and white spindles would look very nice!

Also, I would paint the triangular walls with a lighter grey than the rest of the walls so the volume of the stairs pops up from the rest of the space creating contrast.

dark/black handrail, change your round spindles to square white balusters, they can be decorated modern or traditional.

I do not recommend painting the stair treads or hand rail unless you want to paint them routinely in the future as the paint wears off. if you really want to change their color then I would strip, sand, and refinish them with a grey stain. as for the risers, I can't tell if the risers are painted or if they are stained. if they are painted keep them painted. I'd paint the balusters.

as for the paint color for the baluster and risers, I would paint them the color of your home's trim.

If worried about the paint needing maintenance (spindles are usually fine, it's the railing that may need the occasional touch up in places), you could stain the railing an ebony to still achieve the dark railing.

Kelly please don't paint it. Its a very beautiful staircase, the kind people spend thousands of dollars to upgrade to. Its perfect. Jazz up the walls with paper and grey blue paint or reclaimed wood for a more rustic look. If it ain't broke, don't fix it. Future buyers will appreciate its classic look.