Is a new building financially feasible for us?

I would stay living there with the rent and never buy anything myself. Above all, it is not a [ETW] but a semi-detached house. Buying is not worth it. Invest money in ETFs every month and retire at 50.

Thank you for the breakdown, does it really have to be a 400-450k loan in the end? [....] [....] Wouldn't a house of 130m² for a price of 2,500 €/m² also be possible? [....]

TCountry has class 125 listed as "from 300,000€ turnkey *" on the homepage, which comes out to 2,300€/m². * excluding ground and walls, that's tight with 200€/m². I don't know the scope of services, but I strongly doubt it includes more than the physical house without anything else in minimal equipment. Significant additional costs >10% probably arise during house construction and then everything else around it. It could basically work, but in combination with:

For that, my father is taking care of all the craftsmanship at our place (I have two left hands).

That is an impractical prerequisite, but two left hands can be lost very quickly if necessary. At that price, you rely on own work, including parents/in-laws (never underestimate the wives and mothers on the construction site! They may lack some biceps, but often compensate more than adequately with tenacity.) Labor costs make up about 30-40% of the costs; you cannot save more than that. My personal opinion: Don’t do it. The starting situation of the living situation is a 7-8/10 and will only be improved insignificantly. In return, you severely limit yourselves financially. That might work with extensive own work, but certainly not turnkey. Much too tight a deal and not proportional to the gain.

Furthermore, a Kfw Förderung 300 would be an option for us.

Briefly on that:
KfW300 also means that you have to build to the KfW40 standard, which in turn drives up construction costs – in the end, this usually balances out with the interest advantage.

but left hands are lost very quickly if necessary.

You said that very nicely. I also believe: what is not practiced deteriorates. Whoever doesn’t have to cook for 30 years will eventually not even be able to fry a fried egg in the pan. Whoever is relieved of manual work may eventually not even be able to paint a wall.

[*]Total income €4,750 (€3,000 salary + €250 child benefit + €1,600 parental allowance) [*]Total expenses €1,945.48 [*]Balance €2,804.52

Then increase the savings rate for 2 cars in the costs. €750 is nothing there.

As I already said: mobility costs include more than just fuel costs. . . And then with only one car at about €400 that you have to factor in, you have €2,400 left. And €400 go for ancillary housing costs like electricity, garbage, property tax, etc. The rest is a calculation task with €2,000 and the equity.

For the price you depend on own contributions, including parents/in-laws (never underestimate wives and mothers on the construction site!

In our case, I’m the one who painted the walls. This saved about €8,000. Because “turnkey” catalog prices are starting prices. In the end, you are looking at €3,000 per sqm plus additional costs for a standard house. KfW40 makes it even more expensive; with own contributions you reduce the cost. And with “turnkey” there are also a bunch of invoices in the mid five-digit range overall because turnkey is simply marketing. Nothing more.