Heating not available - Who bears the costs?

I would also consider that the wrong strategy. I want a finished house after all. Nevertheless, I find it worthy of criticism that despite the generally known situation some entrepreneurs act according to old-fashioned "rules" under the motto ham wer schon imma so g'macht. That is only possible because they are still too full. In two years the chaff will have been separated from the wheat, then we will see further...

And then the client also threatens with damages.

Initially, it was only about the question of covering additional costs here. Not about damages in a broader sense. How would it be the other way around if the customer cannot pay? I'm not sure if leniency would apply over months. I think talking to each other but also proactively reacting and looking for solutions is appropriate in the current situation.

And at the moment many craftsmen/contractors are holding back so that construction costs don't run completely out of control...

More likely because they are not allowed to pass it on. Whoever offers a fixed price must also deliver a fixed price. And for §313 the situation is usually not extreme enough yet, plus very few contractors are willing to reveal their calculations to the client so that the client ends up having to pay an additional 5000€.

Much of this also falls under the term "entrepreneurial risk," but unfortunately no one wants to hear that anymore. This applies to all small businesses; the larger a company is, the more it resists this. When you submit an offer, you must first implement everything to ensure you can keep it; if you do not, it will be painful.

Unfortunately, many believe that the painful part should be borne by the end customer, but I see this differently.

In our house construction project, we also involved a lawyer, and currently, it looks like we will only reach an agreement in court. However, it will then be painful for all parties present, as almost everything was documented in writing or communicated by email.

Although of course many people simply ordered the stuff too late. There was no reason for me to order my roof tiles only in March, the building permit had already been available in December. I also don’t want to know when my heat pump or the photovoltaic system were ordered.

Who bears the risk if a storm knocks over a pallet of construction materials or stones in your construction site storage and breaks the roof tiles? Or playing children who do shooting practice with slingshots and stones? The longer you store the stuff with you, the more likely this becomes, and besides the advance payment, the general contractor has to pay for it (which also affects his liquidity). And would there even be space for the roof tile pallets on a tight plot where excavators, cranes, fences, construction pits, and other building materials also want to find their place?

(...) We also hired a lawyer for our house construction project and currently it looks like we will only reach an agreement in court. However, it will be painful for all parties present since almost everything was documented in writing or communicated via email.

Are you already living in the finished house?