Full disclosure: I love the natural grain of wood therefore I would seal it with lacquer if the wood color works with the what you plan to paint the area with. Stain it if you need to .If anything I would paint the base boards on the side the same color of the walls.

Good grief that's a gorgeous staircase. My vote would be to stain & seal. It's very pretty as-is. You paint it and there's no going back (well, without a ton of effort). I hear you on the contrast but I think paint would be a last resort to help cover up disrepair. Your staircase looks to be in great shape.