Balcony / drainage channel at the balcony door needed? No roofing!

No idea if there is a "must". At the normal thresholds like at the TE, I at least have not seen a drainage channel yet.

Balcony is not the same as balcony/ terrace/ flat roof.....

- Attached balconies, freestanding balconies, integrated balconies (loggia), inverted roof as terrace...

For example, the projected balconies already have the water-carrying layer integrated into the structure. Controlled drainage thus takes place within the frame profile. The construction of the steel structure always measures 150-200 mm, thus complying with the aforementioned DIN.

Alternatively, one simulates the hundred-year rain :D and if afterwards everything that should be dry is dry, I don't need an expert/ legal dispute or similar :)

So, the difference is about 6 cm! Does it fit like this, or should there be a drainage channel in front of the balcony door?

Well, it probably should ... You probably don't have planning documents (they would be extremely helpful), but at least a meaningful photo?