Well, TÜV is anyway an inclusive service at KH, so that would be included.
Here are the quotes from the expert's email:
"[...] the range usually lies between approx. 1700 EUR gross (single-family house with basement, project progress without significant difficulties, about 8 to 12 on-site appointments at certain construction stages or key points, little paperwork) and approx. 3500 EUR gross (single-family house, with construction difficulties, increased effort in supervision and correspondence)."
and this:
"
Examples of key points:
- Completion of the subgrade for the base slab
- Completed formwork with reinforcement before pouring the base slab
- Start and completion of basement waterproofing
- Intermediate inspection of the shell construction
- Intermediate inspection of roof construction + roof drainage
- Intermediate inspection of window + roller shutter installation —> sealing levels
- Intermediate inspection of building services water / sewage / underfloor heating, before laying the screed
- Intermediate inspection of waterproofing in wet rooms / bathrooms
- Intermediate inspection of airtightness layers before closing roof slopes etc., with measurement if necessary
- Intermediate inspection of facades + plinth waterproofing
- if applicable, carrying out the acceptance inspection
"
I think there are also experts who are present on the construction site significantly more often.