Hello,
regarding §34:
Type of structural use:
It is obviously a residential area (possibly mixed-use area) and you are building a residential house. Thus, the criterion is met.
Extent of structural use:
The new building must fit in terms of scale. Therefore, it may only have comparable dimensions to those characteristic of the immediate surroundings. The immediate surroundings are NOT just the adjacent buildings. Roughly, everything in direct line of sight can be considered relevant (e.g. buildings across the street). Relevant dimensions are those perceivable from the outside and thus obvious, such as the length, width, and height of the building. For gable roofs, both the eaves height and the ridge height are relevant. Indirectly, the number of floors is also a measure of structural use.
Often forgotten in connection with the extent of structural use is the ratio between built-up area and free plot area. This is basically limited upwards and can be further restricted by the surroundings. The position on the plot is also part of the extent of structural use (e.g. in the case of obvious building lines). The roof shape is not part of the extent of structural use.
The local appearance must not be impaired:
This is a matter of interpretation by the authority. Significant deviations can therefore be regulated, but in practice are usually not relevant unless you are building a neon-colored building.
What can actually be built depends strongly on the exact plot number of your property. If your property is at the marked position of your map excerpt, I would agree with the city and only see a single-storey building there. In NRW, the 2/3 rule applies for full floors; a clever architect with good connections to the building authority might possibly be able to enforce a recessed floor with a flat roof building. On a slope, there is also the possibility to plan a basement with one-sided garden access.
I would no longer consider the house with a flat roof and recessed floor as the immediate surroundings. The house behind the caravan, on the other hand, probably still is.
Best regards