Basement without additional flooring / cleaning floor slab

I would have the technical room tiled (to make sure it’s definitely finished on time) and tile the rest sometime later as a DIY job. Otherwise, you’ll probably have less fun cleaning on raw concrete

The problem will be the already calculated staircase if the distance to the last step is not correct. Or could something still be changed about it?

The child has unfortunately already fallen into the well. To at least get it properly done now, I could also level the floor slab with a leveling compound (a few mm) and then lay tiles or a PVC floor on it. The height of the last step will no longer be correct, but the deviation is very small. Once the stairs are in place, you can measure the last step; it won’t fit perfectly to the last millimeter anyway. Also, how do you want to cover the stairs, or leave them raw?

The problem will be the already calculated staircase if the distance to the last step is not correct. Or could something still be changed about it?

Is it really that bad? Without screed, the structure is certainly no more than 3cm. The deviation is not nice, but in my opinion still OK if one assumes as an alternative that the basement will never be cleaned again. Ideally, of course, this would still be taken into account in the staircase.

I have given your position careful consideration - normally you have to lay at least one waterproofing membrane against ground moisture on the floor slab, depending on the load possibly even as a radon barrier.

I would also tile myself. Cheap tiles from the hardware store laid with a leveling system, almost anyone can do that themselves. The buildup is then less than 2 cm, which shouldn’t cause much of a problem for the stairs. If you don’t trust yourself at all and don’t have anyone to do it, lay PVC flooring. I’m afraid the floor won’t be even enough for just concrete paint. Of course, you can also grind it. But that would probably be more work than the alternatives.

Is it that bad?

Well, I think something like that is called a construction defect. I mean, I think I have read something like that before. Especially when you are only in the few-centimeter range, it creates a trip hazard, which is controlled, among other things, by the brain. So, you feel this irritation when walking the steps, which are supposed to be even. And because of that, one would stumble. But I don't know for sure either.