Construction costs rise by up to 30%

Then there would be no difference to a general contractor, because the common builder does the same thing there.

There is no difference in the costs either.

The architect, on the other hand, only estimates; his profit is certain – not to say, the higher the construction costs rise, the higher his profit will be. In this one point, the general contractor is more of a partner out of self-interest than the architect.

That is not correct! The architect makes a cost estimate in the first step. After further planning stages, precise cost calculations tailored to the individual building are made! At the latest after this meticulous calculation, a contract is concluded with him, which sets and fixes these chargeable costs as the basis for calculating his fee. If anything becomes more expensive in the further course, it is only due to unforeseeable circumstances. However, these no longer affect the architect’s fee.

When the cost calculation is available, you are already in the middle of contract execution or already halfway through the services. Today, no architect agrees to a binding cost ceiling. If by "unforeseen circumstances" you mean that the incoming bids in the tender exceed the estimate, then I agree with you. However, this is currently more likely the rule than the exception.

We initially agreed on [Leistungsphase 1-3] separately. They only account for 9% of the work!

That is not correct! The architect makes a cost estimate in the first step. After further planning steps, the precise and individually tailored cost calculations are carried out! At the latest after this meticulous calculation, a contract with him is concluded, which establishes and fixes these attributable costs as the calculation basis for his fee.

That is one possible variant, "not correct" is wrong. For example, we did not have a meticulous cost calculation – how could we :D. Nevertheless, we reached a clear agreement regarding the fee. And we also only commissioned up to the approval and had help with the tendering.

It is true that building with an architect is often somewhat more expensive than planned. However, this is not due to rising construction costs or poor planning. In 80-90% of cases, it is due to the clients who switch to different materials and fittings during construction. Essentially an upgrading during the ongoing process = higher quality = more expensive.

That corresponds completely with our experience – to attribute a wrong price calculation to our architect would be unfair, only the initial estimates for the earthworks and timber construction were clearly off, but one could still have adjusted the planning. We made the decisions and are also responsible for them. Likewise for a large part of the fittings, which we selected piece by piece during the construction phase. We simply did not calculate how much more expensive than originally planned it was, as this could not lead to any financing changes.
I would not call it poor planning, but certainly an approach which prefers the fun of building and the result over a strict budget adherence. Those who are aware of this can do it without making a mistake. I advise those who are close to their financial limits against this approach.

That is not correct! The architect makes a cost estimate in the first step. After further planning steps, the precise and individually tailored cost calculations for the building are made! At the latest after this meticulous calculation, a contract with him is concluded, which sets and fixes these chargeable costs as the calculation basis for his fee.
If anything becomes more expensive at a later stage, it is only due to unforeseeable circumstances. However, these no longer affect the architect's fee.

So sorry, if you have found an architect who does it like that, then I congratulate you. You have found an incredible idealist.
Of course, an architect does a cost calculation and also does so according to measurements and quantities.
But meticulous and precise? Well.
And the cost calculation is in most cases only done when you are already very far along. By then the plot of land has long been purchased and the financing secured. Because up until then you have a cost estimate.
The experiences of those here may not be scientifically representative, but they probably cover a larger part than your individual experience. And the majority simply experiences that in the end it turned out 10-20% more expensive.
I’m not saying that this is the architect’s fault. Price increases, additional work, change requests etc. may be responsible for this. But the result is just like that.

And yes, I also built with an architect and in our case it was a little more than 10%.