Is it worth having a building surveyor as construction supervision?

I completely agree with you. We are probably so indecisive about whether to choose someone and whom to choose because of our ignorance. Looking for the weaknesses in timber frame construction and then scheduling the appointments accordingly is, I believe, a very good approach.

I have already dealt with the Association of Private Homeowners. Can you recommend them based on your experience and the contact you got through them?

Sorry, your post appeared twice for me, so I made one invisible... it was probably a WWW glitch. The Association of Private Builders charges some small amount semi-annually... afterwards you could cancel again... you also have access to their page, receive letters. No, I have no contact anymore. Regards, Yvonne

Looking for the weak points in timber frame construction and then scheduling the appointments accordingly is, I believe, a very good approach.

Appointments? The classic prefabricated house in panel construction actually has only one weak point: that it cannot be built continuously down into the ground, and at the top edge of the basement ceiling there is always a joint between two construction methods. Many prefabricated house manufacturers have mitigated this as best as possible with their own basement construction subsidiaries. The dimensional accuracy of the basement and the position of the penetrations for stair openings and pipes are things that the prefabricated house company carefully checks during assembly. More difficult here is the legal dimension when something does not fit. These measurements (absolute and in their relative position) can be checked and documented before the house is assembled. Whether this necessarily has to be within this fee range, however, I have a question mark about. Expert fee schedules are not my field.

Well, then I'm relieved that I didn't have a budget for a basement

Just kidding, is that also a topic with the slab foundation?
But that is also sourced through Hanse Haus.

a) Yes, it is essentially the same issue with the floor slab; b) whether floor slab or basement: also from the house manufacturer it potentially always carries one less complication than if it comes from two different sources. The top edge of the basement ceiling (or floor slab) is always the interface between on-site construction and prefabrication.