New single-family house in southern Germany

We have now built our garage/carport directly on the boundary in Saxony with a length of 9m and a width of 6m. Of course, this probably also depends on the federal state and the [B-Plan]. It was a while ago, but my house was in BW at the time, and we also had a 9m basement on the boundary plus the later approval for an open carport extending another 8m. Even the architect had to grin at how that got approved. I want to say that you should probably clarify this best and definitively with the local building authority before you already set yourself limits on the house. Furthermore, I would not advise you to just assume "10x10m" but rather to develop your floor plan first; rectangular floor plans seem to have more advantages anyway, which is why I would also tend toward one. In the end, it might turn out square again due to the floor plan, but then it would make sense.

Somewhere in a carport shop with the 20 sqm in the outdoor area. I have also simultaneously tried the State Building Code BW

An outdoor area (§35) is a completely different matter than the strip of the property outside the building window. As a rule, garages from six by eight to nine meters are unproblematic (and also do not require neighbor approval).

The building envelopes are defined quite generously and encompass practically the entire property. So, we probably won't have any problems with the carport.

Today we came across something in the development plan

The maximum permissible building height is 6.00 m.
The building height is measured, from the building corner, from the upper edge of the ground floor ceiling slab (single-family house - height above sea level) to the intersection of the exterior wall with the upper edge of the roof rafter.

Did I understand correctly that with a gable roof, the upper floor only counts up to about the height of the knee wall since the measurement is taken at the corner?

We also visited the property again today. Development of the area has begun and the first 20m of the future road have already been gravelled.

Did I understand correctly that with a gable roof the upper floor only counts up to about the height of the knee wall because it is measured at the corner?

No.
You have to imagine the outer wall extending higher and the top edge of the roof rafter sideways,
So in the section continue the lines further to the upper left. Draw lines until the intersection of the outer wall and the roof ridge. Understand?
6 meters is not high, but feasible ...

So simply the eaves height minus the thickness of the roof tile? Then it will definitely be difficult with an attic and actually the basement is a must...

So simply the ridge height minus the thickness of the roof tile?

Somehow like that.

Then it will definitely be difficult with an attic and actually the basement is mandatory...

Nope. With KS you have all the freedoms... and especially with a floor area ratio of 0.4. You don't need a third level.