Color choice for steel staircase anthracite - or alternative?

Actually, I initially wanted white and the wall beige. However, by the time we get around to painting the 3-story stairwell, we might as well repaint the stairs too

We lived in our first house (a townhouse) for 18 years. In the meantime, we repainted the stairwell. The stairs didn’t need it. And that’s good because, firstly, you can’t achieve the same quality when repainting that the stairs had originally, and secondly, the effort is several times that of painting the walls in the stairwell. My advice: Decide once and then leave it for a very, very long time.

I am a bit afraid that it will be too dark after all.

A note:
In my feeling, you are looking for the "objectively right color" and I would argue that in such a case there is no "right" or "wrong."
My suggestion:
Try to get as close as possible in your imagination, help yourself with color samples (tape paper strips to the wall) and decide based on your gut feeling.

This may later feel like the wrong choice, for which there is no sure recipe, but this moment is an opportunity to train your gut feeling.