Cracks in stair treads / Cause

That is too dry for wood. At about 55% rH, wood is "stable," 35% rH is a range in which visible drying processes occur, especially if it was significantly wetter during installation in the house.

Then an oak step with a thickness of 4cm tears after 3 weeks?

This is most likely not completely torn. It will be torn superficially and can, as mentioned, recover again with appropriate climate control.

So since yesterday we have a relative humidity of 42%, today it is at 49%. Maybe the low value was also because we only moved in recently, no idea. The stair builder was here and the 3 steps will be replaced. He has the following suspicion. Since all cracks are always at the back right or left and the steps are apparently also screwed there, he speculates entirely on exactly the screw.