Financing for new construction: realistic or rather wishful thinking?

Yes, it should fit well.

But what do you get for T€ 21 p.a.? If that is a 4.8% annuity, that is only T€ 435 in loans (if it gets more expensive, then slightly less - not more).
From that, we deduct T€ 125 for the land and add your equity = T€ 360
It will really only be a small house - which doesn't have to be a bad thing. Actually, think about the usual suspects in the low-budget range and leave out big special requests. Then the deal will work.
Everything offered as turnkey is, by the way, always without floors and wall work. Just so you know and keep in mind that this is always added on top of the catalog prices (besides the other incidental building costs and tasks for the builder).

I ask: as @nordannay says, there would be 360,000, so a small house would be possible.
Are you aware that a house has to allocate space for stairs/stairwell and utility room? In contrast to a 110 sqm apartment, you will probably be worse off in terms of space.

I am probably currently in a situation that you should better avoid. Alone with two children (10, 15), so only one income. Bought or built in 2018/19. My personal household calculation also did not work out as hoped. The installment was ultimately 200€ higher than planned, an income of 200€ per month that then did not come, and so the monthly surplus was significantly smaller than assumed. Since then I have really had to keep track of where the money goes. There are budgets (e.g. for vacation) and I have to stick to them. I consciously allow myself certain luxuries, but more is simply not possible. The car was paid off now, but the money is now being used 1:1 to cover another financial hole. Saving for a new car is not possible. I have accepted that then I simply won’t have one anymore when the current one is no longer usable. Then hopefully I will be master of my time again and only have to get around the big city by myself. Then it just takes a little longer with bus, train, and bike. The children have become significantly more expensive now (class trips, holiday camps, clothes, Germany ticket). The increase in my salary is such that there are still significant real wage losses. We manage, we are certainly not poor, but relaxed is something else. I would like to have a meaningful surplus at the end of the month, but there isn’t one. I put aside a small reserve for the house and other things that one has to replace sometimes. That’s it. Nevertheless, I do not regret the purchase. I am glad to have the house. Overall, though, it was probably 10...20% too much for me (financially).