we went to a prefabricated house manufacturer and informed ourselves at a solid house builder Viebrockhaus
The prefabricated house builder
First of all, I would categorize: solid construction can be a prefabricated house, but generally it is not. Viebrockhaus is not a prefabricated house manufacturer.
Viebrockhaus is a general contractor (GU), who offers you a pre-planned house in solid construction, which can be customized but does not have to be.
Because it is already pre-planned and structurally approved, it is cheaper. However, you can see that it is "off the shelf" (like 90% of all houses).
If you do not plan or want an innovative highlight, you therefore go to a GU or construction company in the region.
Prefabricated house companies usually build with timber frame construction.
So solid and prefabricated construction differ in the material of the walls: prefabricated houses are erected in 2-3 days, solid construction is built with masonry.
And regarding the additional costs: for 185 sqm living space, it should be considered whether a basement is even needed.
Basically, it is not wrong to first inquire about your desired budget.
Regarding the architect: it can be said that the estimate during construction can still increase by 10-20%. However, if you have a "problem" plot, an individual house design is advisable.
There are dozens of discussions on these topics here in the forum, which can be found by searching.