Do radiators always have to be placed under the windows in new buildings?

Exhaust air heat pumps not an option?

I would say, they never really were an option. Except maybe in passive houses.

Heat pump, gas, …

... or dried camel dung? ;-)
I don’t think that new construction projects are currently still being built with gas if the builder is able to use the internet. Gas storage empty, many don’t even offer new contracts, gas network dismantling is starting. Then you need an extra chimney, connection, PV on the roof, only to pay as much for maintenance and chimney sweep as heating with a small heat pump itself costs. I don’t think so.

We are afraid that the FHB has a leak and that something will have to be replaced in 10 years.

First because of costs, then because of leakage... what’s the next “argument”? Is there even a cost estimate, an offer, or how do you know that you save €2793 with “no underfloor heating”?

Are there still these window recesses in new buildings?

No. I also seem to remember that they are bricked up when a house is modernized, meaning rather renovated with underfloor heating etc.

We would rather not lay (have laid) a screed in any form. We are afraid that the underfloor heating has a leak and something will have to be replaced in 10 years because of it.

I can't quite believe that "argument" either. What about running water? Or the electrical cable that could be drilled into and only after years might cause the house to burn down? Do you want everything installed openly on the surface? Some fears are irrational and hard to understand.
Because in the end a leak would only be an insurance claim and a good opportunity to change your flooring again.

We are afraid that the FHB has a leak and that something will have to be replaced in 10 years.

Underfloor heating pipes are laid endlessly. There are at least no screw/crimp/press joints that can become leaky. And the probability that an underfloor heating pipe lying peacefully under the screed will suddenly become leaky is zero. If leaks occur, it is because a craftsman might have messed up and damaged the pipe – but then it does not take 10 years; it becomes apparent when heating up during the construction phase.

since we, although we are really building a completely ordinary house, have partly deviated from the mainstream;

I have doubts whether it should only be due to my eyesight that I have not noticed any mainstream deviations so far. Your initial plans disappointed me greatly, and up to now I only harbor hopes in gardening that something might still come. When we once talked here somewhere about faschen or other window frames, I was already looking forward to helping you design a beautiful facade. And then unfortunately nothing came, just the usual plain rectangular cutouts from the simple wall, except vanilla instead of white. So far I unfortunately only see plain vanilla zero eight fifty point zero zero zero one :-(