Floor plan: Staircase planning steps in the turn

The sketch shows 2.95m.

However, the sketch does not show the OP's staircase, but is from another thread here

This is now a very poor graphic (not to scale and stolen from another thread, sorry) and maybe it doesn't even help, but the staircase was planned this way to have headroom.

I have to honestly say that the post only confuses me even more.
An EG and an OG are posted, showing that the stairwell might be too small.
Then this here

This is a stepped area; the lower half has normal floor height, the upper half is about 1-1.3 m high, basically a landing. This is not visible in this drawing. The headroom is given.

According to my scaling, the staircase is overbuilt by 1.87 in length. That roughly translates to a height in the EG of 150 (my program cannot do this, so these are only approximate values), where the stair step is at 1.87 height. This leaves a height of 1.62. Adding 20cm ceiling thickness, we are just over 1.80. Even if the edge there should be chamfered, it is not enough.

Regarding the question: I seem to have heard that one should design the windings symmetrically because it is easier for the body and brain to navigate the staircase. But that might also be false.

At least a section belongs to this planning. Furthermore, the staircase builder will have a more detailed stair plan or will still make one, where it is explicitly visible how deep the steps are, etc. I cannot imagine that the architect already plans the feasibility exactly in this stage. The staircase is basically a placeholder.
In the detailed planning, you can then also see how much tread area, i.e., depth the chamfered steps have within the walking width, i.e., in the middle.