Is the price increase for the general contractor after signing due to raw material shortages lawful?

I believe you are under false impressions or are you perhaps from the industry?
Especially to the big main contractor, you as a small builder who maybe builds a house once in a lifetime, don't matter. If you try to make bad press, you will be sued into the ground by the legal department – conversely, if you sue them, they will delay you until you run out of steam...
The small one may be more concerned about his reputation, but just look at how many reviews you really find from small main contractors. The small number of houses is a protection against the algorithms on the internet. There simply isn’t enough relevance.
Losing you as a customer does not matter nowadays. It is a seller’s market because everyone is building. Prefab house manufacturers have waiting lists of a year or more, whereas the local solid house builder who can start immediately as soon as the building permit is there, is super attractive.
The craftsmen jump from site to site and can afford shoddy work that is outrageous.
You are at the very bottom of the ladder and can only try to dodge the biggest pile of crap with an incredibly flexible spine...

I think you are under false impressions or are you from the industry?
Especially for the big general contractor, you as a small builder who maybe builds a house once in a lifetime, don’t matter. If you try to generate bad press, you will be sued into the ground by the legal department – and vice versa, if you sue them, they will stall you until you run out of steam...
The small one might care more about their reputation, but just look at how many reviews you really find from small general contractors. The small number of houses is a protection against the algorithms on the internet. There simply isn’t enough relevance.
Losing you as a customer doesn’t matter nowadays. It’s a seller’s market because every Tom, Dick, and Harry is building. Prefabricated house manufacturers have waiting lists of a year or more, while the solid house builder around the corner who can start as soon as the building permit is there is super attractive.
The craftsmen do site hopping and can afford botched work that is really bad.
You are at the very bottom of the ladder and can only try to dodge the biggest pile of crap with an incredibly flexible spine...

No – definitely not.

As I said, I know it from my own experience with a lawsuit against VW. VW gave in, because they don’t eventually run out of steam, but financially it just no longer makes any sense – it’s simply a fact.

Bad press is one of the worst things that can happen – even the legal department can do absolutely nothing about it! For regional companies even much less!

The only point I agree with you on is the waiting lists – because of that, a construction company can afford a lot more. However, all these facts do not change anything about the approach in such a case. There are always individual cases – but looking at the whole, you are simply to blame yourself if you always see yourself as the "little guy" :)

This has nothing to do with the construction industry at all... No matter which industry, the philosophy of a company or its economic viability is always based on the same values – depending on the company’s management.

Believe me... You get away with so much more than you think :)

And above all, this discussion is about a current market development – it concerns currently planned houses with fixed price contracts. The time for that is going away? The new offers with 10% extra costs are already running? Believe me... The current projects just get carried along – anything else would be total nonsense

They are often neither checked for entitlement nor for correctness of amount. Next lesson learned from the builder.

is in many cases not possible either! Therefore, you simply have the shorter end of the stick there.

In conclusion on the topic from me:

If such a situation occurs with a client, they may of course decide at their discretion. Maybe the money is easily available and one agrees to the demands? Perhaps one is just that type of person and doesn’t feel like negotiating, or is afraid that their project might be jeopardized as a result?

No question... Everyone has to decide that for themselves. For my part, I just want to point out that especially in the current market situation, one shouldn’t accept everything and should only partially comply with any demands from the [GU].

You don’t always have to settle this directly through a lawyer... With some negotiation skills and a bit of "firmness" one can find a proper solution otherwise as well. If the [GU] was carefully chosen, you have certainly established a trusting contact and can have a proper discussion about it :)

Regarding the margin, my partner’s favorite joke is: two school friends meet again after a long time. One of them is doing well, but he wants to make the other understand how difficult his business is: "oh, you know, I became a dealer. I buy things for one dollar and sell them again for six dollars – and from the five percent *traurigemienemach* I have to live."

Even if it sounds to me only moderately like an insolvency risk here if the original poster stands firm: IF insolvency occurs, the builder becomes the usually very subordinated creditor and therefore the last one to be bitten by the dogs. Insolvency administrators are contractual partners for someone who has killed their father and mother, you wouldn’t wish them on your worst enemy. So the original poster should check the value of their completion guarantee before making a decision ;-)

The fewer trades the general contractor can cover with his own people, the more likely it is that the case will arise that he can commission the core subcontractors for the builders who share the price increase and try to "buy at the old conditions" for the contract bullies by gambling whether the "cheap Jakob" might also complete the trade without complaints.

How "tough" a builder can remain therefore also depends on the "height of the fall" of the equipment, i.e., the quality risk is shelled and naturally higher with rocket technology air conditioning than with plaster and gas boiler. The supposedly avoided additional costs might possibly have to be spent easily on the cost center expert visits if you then have to check whether the cheap drywall contractor is just botching the soundproofing mats.

And above all, this discussion is about a current market development – it concerns currently planned houses with fixed price commitments. Time is running out? The new offers with 10% additional costs are already underway? Believe me... The current projects are simply carried along – anything else would be complete nonsense

but we are talking here about an unpredictable market development that will still have some consequences. It is difficult to insist on a small general contractor’s right and say that he will recoup his lost margin elsewhere when this general contractor currently cannot accept orders because the procurement of materials for the future is uncertain. Compared to an example from acquaintances where a large general contractor made a mistake because the lintel was forgotten to be calculated on the windows and the additional costs were then attempted to be passed on to the client, this is something to be viewed more differentiated here. In my opinion. You always compare with large companies and situations that have nothing in common with this.