Wauw, I like your way of doing stuff - especially the before and after graph… this is a data scientist at work.
My situation is similar: it’s a house from 1840 which we completely renovated and isolated. We have large windows on the south side and these interfere a lot with the generic thermostat.
As for heating, I have a Itho Daalderop Central Heater (instead of your stadsverwarming) and for each room, I can control the valves of the underfloor heating. All is controlled by HomeAssistant.
- If any room is requesting heating, the valves of that room open and central heating is turned on.
- If no room is requesting heating, the central heating is turned off.
The valves itself are thermo-electric (e.g. candlewax valves: https://en.wikipedia.org/wiki/Wax_motor). The response times of the valves is about 2-3 minutes to open and 10 minutes to close.
So, my gut feeling says:
- The PWM won’t work as response time of the wax valves is too slow / I have fear the wax motors will die faster if I use PWM
- The influence of the sun/weather is large due to the windows on the south side and should be taken into account
And to be honest: I don’t know anything about a PID thermostat 
. I should put it on my todo-learning list soon but my gut feeling says it won’t work due to the external influences. Or am I wrong?