Air-water heat pump + central ventilation system with active cooling - Which one?

But the air conditioning needs significantly more electricity than a controlled residential ventilation

Overall, an air conditioner doesn't need much electricity if you operate it properly. That means turning it on before it gets too warm and only turning it off again when it is cold again. So just let it run. For 140 sqm of partly renovated old building, that's no more than 500 kWh per year for me.