Is it permissible to exceed the eaves height of a semi-detached house?

In post #1, drawing 2, I see something completely different than what you present in the text: namely two adjacent plots of land each with a detached single-family house and by no means uniform ridge directions; and above all, no heights can be seen there. I cannot follow you in the slightest.

The eaves height is not simply measured but calculated by an expert. Whether the roof pitch or the ridge height plays a role - I do not know how the calculations work.

Far from any witchcraft. The eaves height is the height at which the exterior wall breaks through the roof covering. So it is as if you did not hang the eponymous gutter at the actual end of the roof surface, but imagined the roof overhang away and let the roof hypothetically break off exactly at the outside of the exterior wall.

In post #1, drawing 2, I see something completely different than what you describe in the text: namely two adjacent plots each with a detached single-family house

No. Two semi-detached houses are drawn. The roof ridge directions are not apparent from the drawings, only from the post. On the left, each half has its own roof, which then meet at the eaves. On the right, a conventional semi-detached house. As already stated.

Two semi-detached houses are drawn.

Aha (?) - but each on single-family house plots (35 / 240/17 and 39 / 240/16). Accordingly, they are probably rather two-family houses, whose side-by-side or back-to-back apartments do not have their own plot.

I think it has something to do with the shape of the roof.

I believe it has something to do with the development plan. It should define what is meant by eaves height (usually what describes in #7) and where the reference point is. There are big differences here. Some development plans refer to the natural ground level at the exterior wall, others to the planned development height of the access road. In the section drawing of your first post, the eaves height according to definition #7 is at 4.438 above planned ground, in the section from post #3 it is at 4.00, with planned ground seemingly equal to the reference height of the street. So either make the development plan accessible to us or check how the eaves and the reference point are defined in the development plan. If the conditions for both properties are indeed the same, a 43.8 cm exceedance might also qualify for an exemption. Then only an inquiry at the approval authority will help.

The planned expansion height of the access road is correct.

Both conditions are exactly the same. The same regulations apply to both properties.

So it has nothing to do with the fact that higher construction is possible due to the roof shape? That is also the case with houses with a stepped roof.

So it has nothing to do with the fact that higher construction is possible due to the roof shape?

I still haven't understood what you are getting at. In your examples, the roof shapes are the same – both are gable roofs with the eaves on the sides.

It's also the case with houses with a stepped roof.

What do you mean by stepped roof? Stepped floor with flat roof? There the eaves height = parapet.

Both conditions are exactly the same.

So street level and plot level are exactly the same?