Is financing a new single-family house feasible?

Saving is okay, but who wants to put used "junk" in or hang it in their new home…

I do, because not everything that is used is junk. I am very much in favor of second hand (almost all my kitchen appliances were bought used. My kitchen with 7 linear meters cost about 8000 euros). Otherwise, a terraced house would be something. You don’t have to buy so much land and later pay less property tax. When I read: "the neighbors are on my back," that is firstly not very social and secondly, they are on your back even if they are 10 meters away. The difference is really not that big. If you have to watch your finances a bit, besides the tips mentioned like leaving out the garage and buying second hand, it also helps to keep the regular costs low. A smaller plot of land would be advantageous. (My plot is 18x6 which is enough for a garden feeling. And that also keeps regular costs and effort low).

I see it the same way. Due to the sharply rising interest rates, your net income is unfortunately too low for a loan of €400,000. Currently, I see an interest rate of just under 2.6% for a 15-year fixed interest period at a loan-to-value ratio of 100%. This would be a monthly rate of €1,686. Most banks assume costs of €2,350 per month for 2 adults plus 1 child. In addition, the warm rent is calculated. Let's assume €700 here, then your disposable income for the loan installment with a net income of €4,000 would be €950.

These are exactly the crucial points - garage or not - construction costs are currently at best minimally predictable, a buffer of 10% should always be included. Today more likely (unrealistic) 20% or more. I do not see that here. The necessary credit limit would already be at the limit for the household income, and the monthly burden far too high. Healthy would be maybe €4,300 / 3 - €1,400 - I absolutely do not see that here. Do not forget, life will get more expensive, and banks will also take the increased additional and living costs into account in the calculation. And even if not, one should do it oneself.

The costs for children are indeed greatly underestimated here. Just for clothes alone when the child keeps moving up a size. Or try buying a few decent shoes for the child (Lowa etc). You’re easily spending between 70-100 euros. And what happens then? Shoes broken after 2 weeks because the child drew on the floor with chalk. :p We also once bought 2 pairs and after 3 months we needed a different size again. The monthly budgeting here is partly significantly too low.

The costs for children are indeed totally underestimated here. Just with clothes when the child changes to a different size all the time. Or buy a few decent shoes for the child (Lowa etc). That will set you back between 70-100 euros. And then what happens. Shoes are broken after 2 weeks because the child drew on the floor with chalk. :p We also once bought 2 pairs and after 3 months we needed a different size again. The monthly cost planning here is sometimes significantly too low.

We have four little money-consuming machines at home... When I buy shoes for all of them at the same time, the shoe salesman almost faints with joy... :)

I agree: Children are expensive and more expensive than you think beforehand...

Yes, children definitely cost more money than some might suspect. But, for example, when it comes to daycare costs, one should not generalize from their own experience to others. There are huge differences. Depending on the federal state or even the municipality, there are significant variations. For example, the daycare place for our infant cost €145 and currently, the daycare place (although half-day) costs only €18 per month.
You can also talk to your employer about whether they would cover the daycare costs instead of a salary increase. This offers benefits for both employer and employee as it is tax-advantaged.
Nevertheless, I see all of this here (unfortunately) as far too tight. a) the costs are calculated too narrowly b) the times are not predictable and turbulent and c) the monthly rate here absolutely exceeds the comfort zone.

We have four little money-destroying machines at home... When I buy shoes for them all at once, the shoe salesman almost faints with joy... :)

I agree: children are expensive and more expensive than you think beforehand...

I still have a statistic from 10 years ago in mind: A boy costs on average 500,000 EUR, a girl 600,000. On average in Germany including all incurred costs until... well until... they leave the house?!