Cost of cisterns, systems for collecting/retaining precipitation

The design is determined by the roof area to be drained. How large the cistern had to be and how much retention we must have was done by our architect together with [Firma Mal].

My construction company estimated about €4000 (external company) and reported that they also had a case nearby where, in the end, due to building regulations, it even became €8500 (2 pumps, throttling & buoyancy protection).

Unfortunately, no one in this forum will be able to answer that for you. The calculation of the size has different influencing factors (you can also find some calculators with Google), which we unfortunately do not know here. We also cannot contribute much here regarding your water level (due to buoyancy) and your desired equipment (pumps, etc.).