Prefab house - yes or no?

According to what we were told, it is indeed easier to meet KfW criteria with a prefabricated house, but if the heating fails, the house also cools down very quickly

But that is exactly the opposite of what the U-value of the walls means. The better the insulation of the wall, the longer the heat stays in the house. It doesn't matter at all whether it is solid or prefabricated timber frame. By the way, it is the same for us. In the first winter, we had no heating at all during the interior finishing and still the house maintained the temperature very well at at least 12°C. Even when our heating failed once (due to a flow error), I only noticed it because I looked at the temperature display in the bathroom and it showed 1°C too low.

After airing once, it is cold and remains cold because there is little to no energy stored in the walls that could reheat the rooms...

After airing out once, it is cold and stays cold, because there is little to no energy stored in the walls that could reheat the rooms...

My experience contradicts that. But if it is actually cold outside, what warmth do you then have stored in your walls? Because heat is released to the outside in winter as well, not just to the inside.

I cannot confirm that either! Presumably, a significant part of the heat is also stored in the screed. Regardless, I wouldn't build without [Kontrollierte-Wohnraumlüftung (mit Wärmerückgewinnung)] nowadays. That also eliminates the need for airing out in the freezing temperatures at the moment.

Then airing out is also unnecessary in the freezing temperatures at the moment

Correct, that has also proven successful for us. I wouldn't build without controlled residential ventilation anymore. But you have to get used to keeping the windows closed first.

So, the low heat storage capacity of the walls is even advertised by the prefabricated house factories. Scanhaus Marlow Marlow in the brochure: Heats up faster in winter, cools down better overnight in summer. That cannot be denied. That is how it is. Those who want that can get it at Scanhaus Marlow Marlow. Those who want the other have to build massively.
Regarding the building services: What is not there cannot break. As little as possible. Gas boiler plus, but only because they force us to!, solar panels for water heating. That would be my advice. Control technology is prone to failure. All those systems for who-knows-what just end up pleasing the heating specialist afterwards.
You can surely just open the window and ventilate.