Slowly but doubt about financing

If the current state does not allow construction, but the view promises it, then only saving (or inheriting, or winning the lottery) helps, or you find a cheaper existing property.

However, this only applies if you consider saving in isolation and disregard the framework conditions. In our case, "waiting and saving" would mean that in 5 years we have about €60,000 more equity, but at the same time have wasted €60,000 on rent. The deeper meaning of not immediately putting the €60,000 spent on rent into the home is unclear to me.

I am not saying that saving is generally pointless. However, if a financing plan is already calculated with a very tight budget and might just work, meaning the income is not very generous, then usually one cannot save enough on top of the rent to more than compensate for the increases in costs.
Just as an example, including all the increased costs, our house would today probably be about €40,000 more expensive (also due to the newer energy saving regulations) than it was 3-4 years ago, which is about 10%.
That means one would have to save about €10,000 per year plus continue paying the rent. Additionally, as mentioned, there is the risk of rising interest rates.
Anyone who cannot afford a €400,000 house today most likely cannot save at least €800 plus pay rent at the same time.
However, someone who is maybe in their early to mid-20s, lives with their parents rent-free, and is just starting their career can, or indeed should, save because salary increases are to be expected.
Therefore, one can never say it outright, but anyone in their mid-30s who cannot afford it now will hardly be able to afford to build in 5 years either, unless something drastic happens.

Well, that's just how it is here. Elsewhere in the world, 12 people from 4 generations live on 25m² and here it is impossible to live with 3-4 people on 120m²
You don't even have to go that far, even in big cities families with children often live in a 60-70m² 3-(small)-room apartment.

It's bad enough that people from elsewhere all want to come to us.

Of course, if you live in a big city, you chose it that way. But in the countryside, a few different rules apply. I always find it quite funny when you have to drive the lawn mower through the living room to get to the garden.

However, this only applies if you look at saving in isolation and ignore the framework conditions. In our case, "waiting and saving" would mean that in 5 years we have approximately €60,000 more equity, but at the same time have wasted €60,000 on rent. I do not understand the deeper meaning of not immediately putting the €60,000 for the rent into the home equity.

Honestly, I can't hear these arguments anymore. You don't save so that building a house ends up being a few percent cheaper, but to minimize personal risk. This is extremely important especially with smaller incomes and thus low repayments below three percent.

You don't give away rent, but receive a value in return that is at least materially higher than when building a house. Materially speaking, one would have to say, why pay x thousand euros in installments when I can live in rented accommodation for significantly less per month.

When building a house, the main thing that counts is the ideal value, and you have to be able to afford it or finance it with manageable risk.

willo has hit the nail on the head. I have now given up presenting the corresponding arguments. There are pages of threads on the topic here.. everyone should do what they want

Ultimately, everyone can only decide for themselves and merely ask other people for their opinions.
The income of the OP is not that low after all; with the omitted bonuses and side job, he has over €5000 available per month!
Besides, he has a decent buffer and has rather generously estimated the additional costs and there is certainly some savings potential regarding the size of the house, so he could also manage well with €60,000 - 80,000 less, which would result in a loan of slightly over €420,000. Depending on the interest rate (assumed about 2.3%), this results in a monthly installment of €1600 over a 30-year term, which is definitely manageable with his income.
The opinions and views are simply too different; one person is a civil servant and doubts whether a €2000 installment is possible with an income of over €8000, others together only have €3500 and pay €1500 per month just for the house.
You simply have to make an honest assessment and then decide for yourself; no one can take that away from you.
I also know people who have a five-figure income, rent their place, blow all the money on vacations and clothes, and drive an old French compact car. Everyone has their own priorities like that.