Buy land with a variable loan?

Whereas T€ 250 for the house construction is probably just wishful thinking.

Then there are still additional building costs, exterior facilities, carport, paving, and kitchen missing.

Nonsense. You buy from and build with completely independent parties. So only real estate transfer tax on the purchase. It has always been like that.

If that's the case, I'm of course happy about it! I had read about it several times.

The €250,000 was a fictitious example to understand at all how the conversion from a variable loan to an annuity loan works / what happens there. (I am aware that €250,000 is too low.)
Unfortunately, I still haven't understood it.
I just want to first understand how high the new loan amount is in my (fictitious) example after 12 months when converted into an annuity loan and how much equity capital has been contributed to the financing (which seems to be €45,000).

Equity then corresponds to the value of the property minus the outstanding loan amount. In the example, that would be about 45K, unless the property value changes drastically. The new loan is a completely new contract; it is usually not really "converted". You can also sign with a completely different bank, which is exactly the advantage of variable financing: you can easily get out of it again.

I first just want to understand how high the new loan amount is in my (fictional) example after 12 months when converted into an annuity loan

Then read my post