Floor heating setting - desired temperature

that is already done by the AT regulation.

The AT specifies a possible heat demand, which does not necessarily correspond to the actual heat demand, since only the outside temperature is taken as the basis, and all other boundary conditions (solar radiation, wind) are not considered.

The return temperature can certainly be included as an additional parameter in the control. But only if the flow rate is measured simultaneously or is always constant.

Which flow rate is recommended for 5 heating circuits? Living room / dining room / kitchen better a high flow rate, meaning 3 liters, or rather only 1 liter?

You will have to try that out. The rooms with higher heat demand and/or less heating surface receive maximum flow. These are almost always the bathrooms. You regulate the supply temperature so that the desired temperature is easily reached here (RTR switches off). You throttle the flow in the other rooms until the desired room temperature is no longer reached, and then open it up a bit again. The whole process takes time because the system is very sluggish, and you should wait at least 24 hours after each adjustment.

For some users, the heat demand on the upper floor is still supposedly higher than on the ground floor, so the flow on the ground floor is the lowest.

I have 4 l/min in the bathrooms and about 1 l/min in all other rooms.

The documentation from your heating installer should also include the projected flow rates. This is at least a starting point.

Thank you very much for the detailed answer. I have now set the flow rate in the living room / dining room / kitchen to 1 l/min. RT is set to level 4. In the bathroom on the ground floor as well as the bathroom in the attic, I have set the flow rate to max. 3 l/min in both rooms means RT is at 6, i.e. fully open.

Small interim result after fiddling with the pre-run screw for 24 hours. The apartment is still warm. You can also shower well with 50 instead of 60 degree hot water. Maybe the thing with legionella is also overrated? Or how high do you set your hot water?