Is it feasible to buy a second house with a mortgage on the first house?

Anyway - it is an idea to consider. I am familiar with what it means to found a company as a partnership or corporation, to sell it partially or entirely, to close it in different ways, or to keep it empty in stock. As I said, it’s all not rocket science.

Very brief update:

The bank offered us an interest rate of 3.58% for 10 years. With €230,000, we would have a 900 payment. (Without a mortgage on the own house. Income of a total of €3200 assumed, which is not a problem.)

What is your general plan now? In the initial post it says something about 2200 income (potentially more). I was thinking now: * Re-entry (potentially earlier?) * Then to get financing and purchase finalized It's not explicitly stated anywhere just always that the income is not a problem now after all

Very short update:

The bank offered us an interest rate of 3.58% for 10 years. For €230,000, we would have a €900 installment. (Without a mortgage on our own house. Income of a total of €3200 assumed, which is not a problem.).

With a €900 installment at this interest rate, you would still have a remaining debt of €199,000 after 10 years.... Are you sure that a bank agrees to a repayment rate of 1.1%?

With a 900 rate at that interest rate, you would still have an outstanding debt of €199,000 after 10 years.... Are you sure that a bank agrees to a repayment rate of 1.1%?

The bank offered us an interest rate of 3.58% for 10 years. With €230,000, we would come to a 900 rate.

I would claim that the bank did not agree, but offered. With the repayment, you end up with a term of 40 years, which is absolutely common (whether it is good, nice or whatever, is another question).

The fact is that we manage with the currently available monthly income and our costs. However, currently nothing is left over. Understandable. (I still have some equity from which we finance our vacations, etc. I do not want to include this reserve in the calculation.

At the moment you are, as you yourself write, partly living off your savings.
Then there are somewhat shaky additional income of 1300€, but this is offset by a loan with about 1% initial repayment and a 900€ installment, plus non-allocable ancillary costs and repairs.
The savings of 70,000€ (which you reportedly did not want to touch) will probably be reduced by 40-60,000€, depending.
(20,000€ for the difference purchase price-loan, estimated 20,000€ for ancillary costs, and then gift tax)
I personally still find it insane.