New construction + exhaust heat pump according to the builder, is a trench collector affordable?

I simply find such systems not practical in areas where the plots are hardly larger than 400 m². As a result, there is no way to avoid disturbing the neighbors with the noise.

The statement that "such systems" (air-to-water heat pumps) are not practical in dense housing is a bit of a generalization! At least for devices that are installed inside the house, this problem should not apply. So the possibility does exist.

I find a constant noise even worse than occasionally passing vehicles.

Best regards
Sabine

If the device is constantly making noise, something must have gone seriously wrong. I still remember how I definitely wanted to hear how loud the unit was at my place. It took forever until I finally stood in front of it when it was really running. You couldn’t hear anything from the neighbor’s terrace anymore.
When I come home in the current weather today, the heating control shows me that the pump last ran 10 hours ago. For a few minutes.
In summer, it will hardly run at all. Hot water then comes more than enough from the roof.
Noise disturbance is something else.
In addition, when the pump runs more often in winter, hardly anyone sleeps with the window open or feels disturbed in the hammock in the garden.

Seriously, before construction I was also concerned whether it would be too loud and disturb neighbors; perhaps cheap loud devices are installed wrongly here and there. But what I have heard and seen from friends/acquaintances convinced me, and there is certainly no basis here for generalizations that air-water heat pumps are loud and disturbing.

In our street, someone has an air-to-water heat pump in the utility room and two air outlets to the outside, one facing the street, the other towards the neighbor. When I approach this house, I can hear the noise from about 15 meters away. Is that normal, right?

Best regards
Sabine

In summer, it will then hardly run at all. Hot water then comes more than enough over the roof. Noise pollution is different.

However, most have omitted the uneconomical solar modules by using an air heat pump.

It's not always just about economic efficiency, but that's another topic. Even when the pump has to produce hot water in sunshine, it doesn't become a continuous hum.

So I have been using an air-to-water heat pump for three years and am super satisfied.
Heating and hot water costs €65 per month / all year round.

Bathroom/living room temperature around 23° Total living area approx. 200m²

Noise disturbance? When I stand on the veranda at night and hear the oil burner pump start up in the neighbor's house, I hear it (through the chimney) somewhat as loud as my heat pump. And in summer it hardly runs at all and in winter the windows are closed anyway.

PS: I have dispensed with a ventilation system - I didn't like it.