Wood/steel staircase or a concrete staircase covered with wood?

My husband had the same thought. I just thought that you never really reach the riser, since you usually walk on "tiptoes" on the stairs

Right, but then you go over it with the vacuum cleaner or the mop... We now want to paint a strip as high as the baseboard on the wall next to the stairs with "elephant skin." That might also be a measure for white (plastered, painted) risers if wood is not desired there.

A photo for illustration (old/new) by the way, the side of the stairs is still covered with gypsum fiber, so the stringers won't be visible afterward.

Would you like to upload the picture here as well? I'm curious after the description but don't see any picture (somehow the upload server isn't working).

I'll give it a try!