A beautiful stair runner would do more for your stairs than molding. These are just examples, but if you go this direction then choose a palette that harmonizes with your space.

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stairs get you from here to there -- they don't need to be gorgeous unless they dominate the entranceway. I'd add better lighting and call it a day.

I agree with housegal. Add a runner.

In itself it is a beautiful staircase. It needs some texture and some interesting lighting. The choices are overwhelming. Here are some ideas:

That is a really good point. I had carpet on a staircase before too and you are right. They are a pain to keep clean and hard to vacuum! I would have never thought of the lights either.

I love this look. Could it work here?

Sure could you make that there. As long as you think of enough light as well, for the staircase seems to be very dark, even with the light paint.

Suggest adding a large framed picture upstairs facing the stairs to draw your eye up. While the picture arrangement up the stairs looks great, since it’s a closed staircase, I don’t think you would see them. You could install a hand rail on your other wall for balance.
Lovely staircase already.