Straight staircase for single-family house: Are the dimensions okay?

Why don't you make a 3 cm overlap? Then you don't need the 4 m.

Because the 3 cm overlap when going downstairs does not matter and thus makes the tread surface very small.
Once again my staircase picture ... note that only floor heights of 280 cm are considered here

It is already comfortable over a length of more than 4 m.

Define story height and stair height! Note: story height + ceiling height is stair height

.. I disagree here ;) .. from Wikipedia and also my understanding as well as usage in various CAD programs:

The story height in buildings is defined as the vertical distance between the upper surface of the floor of one story and the upper surface of the floor of the story above. The story height results from the addition of the room height and the thickness of the ceiling above.

==> Stair height = story height, you just have to make sure not to consider only the room height.

EDIT: Nice picture for this

I didn't know that. Thank you!

@ : I found the calculator you used. The comfort formula is calculated by subtracting the depth from the height of the step. The result should ideally be 12 cm. Therefore, with a depth of 27 cm, the height may "only" be 15 cm. This, in turn, means that with a floor height of 2.97 m, you need 20 steps, so the staircase must be 5.40 m deep. Conclusion: I believe this comfort formula is too strict for the "average Joe" :)