The children's room is too warm in the new building.

For me, that means I couldn't heat any warmer via the thermostat even if I wanted to.

Yes, that is exactly the goal. That’s why during the balancing process, leave the thermostats alone and open them all fully. There should be continuous flow in all rooms. For heat pumps, the recommendation is to completely remove the thermostats.

If it really gets too cold at -10°C, you will adjust the supply temperature accordingly. According to DIN, 35°C is the design temperature; for you, it was planned with 40°C. No big deal with a gas heating system. You will find out what is sufficient when the time comes.