Single-family house with 160 m² - development plan, living area calculation

And a shower under the stairs is also a typo? Well, then I am relieved

No, that was not a typo, but an idea that I wanted to evaluate here.

The idea: A concrete staircase, under which there could be space starting from a certain dimension, which would then be used as a shower.
In some floor plans you often see that the space under the stairs is used as a storage room – so why shouldn't that be possible here? Not the entire shower under there, but using some space.

Maybe the sketch helps here (proportions are not correct!):
On the left "normal", on the right with the red box the idea. The side view is also meant to clarify the area.

The question was whether something like this is possible and whether it makes sense.

For various reasons, I would consider this rather nonsensical. - you would have to design your entire floor plan around the bathroom being in this location - as you have drawn the staircase, the corridor would be at the top of the plan, so the bathroom would have to occupy almost the entire lower half of the floor... - usually, a wall is needed on one side of the staircase - the free space under the staircase is generally larger than a shower, so a storage room or built-in closet is more space-efficient