Construction costs are currently skyrocketing

The architect told us that the current construction prices per sqm are 4,500 euros turnkey based on currently ongoing BVH,

Everything just standard and nothing extravagant...

Seems way too high to me. For example, I recently heard 3k/m2 at Schwörerhaus from people I know. Sure, there are additional costs etc., but even with a lot of custom work, 4.5k/m2 is still too high. We are building with separate contracts and are currently still getting some offers; despite high standards, we are far from 4.5k. I would contact more architects/providers.

It is simply a very unfortunate time. Two years ago you probably would have managed everything wonderfully. But in your place, I would contact more architects.

For that, I'll also build you a nice little house and treat myself to a fat 911 from the profit.

It's always a matter of perspective.

But €4,500 is just as unrealistic as €2,000.

Including materials? That’s really very cheap

And you are wrong there. Living is something different from a sports car or a yacht. Construction prices, purchase prices, and rental prices are not 3 completely different things; they are connected. When construction and purchase prices soar, this also affects rents in the medium term. And that concerns everyone because everyone has to live somewhere.
Moreover, a well-functioning society should enable everyone to live well: in an apartment that does not consume huge sums for heating, in an area that is quiet and safe at night, and where there are no broken glass shards on the playground. Ownership for everyone is not necessarily required to achieve this, but ownership protects to a certain degree against extreme price increases in the housing market. As I said, in the medium term this is not decoupled. A landlord does not rent out of charity but to earn something with their money. And even if the apartment has already been paid off, renovations are due eventually, and then construction costs will also be reflected in the apartment.

Sure with material and yes, that was already a good price. 120€/m is simply usury, at 70€ my fuse would have already blown. Two years ago I paid <50.