Cracks in stair treads / Cause

There is a gap on both the left and right sides to allow the wood to expand.

Between the (masonry?) "cheeks," I assume.

The treads are attached to the concrete with a kind of adhesive foam.

So not floating or sliding - no further questions, Your Honor! :-(

Between the (masonry?) "cheeks," I assume.

So not floating or sliding - no further questions, Your Honor! :-(

I am not a contractor, just a customer. What does that mean?

I don't really see a problem there either, since assembly foam is flexible, it should accommodate the natural expansion and contraction behavior of the wood. I also think that moisture first, and then strong dryness, are responsible for the cracks. Up to a certain degree, this is normal and can actually go away again. Get yourself a hygrometer. Whenever the humidity is below 40%, turn on a humidifier.

I am not a builder, just a customer. What does that mean?

By the masonry stringers I mean whether the staircase is basically clamped between rising walls and only has room to expand at these points.
Floating means lying freely movable on a substrate; sliding means fixed at one end and movable at the other (e.g. screwed on the left in the round hole and on the right in the oblong hole).

Above all, play on the left and right is rather pointless. The expansion of wood in the longitudinal direction is minimal compared to the change in dimensions in width.

The hygrometer shows humidity of 35%, measured on the stair step.