House purchase possible? Your opinion

Definitely get an expert who goes through it with you. You don’t want any nasty surprises. I find the price quite low for such a well-equipped place. Of course, it also depends a lot on the location.

For a half-timbered house, I would always recommend having a building expert who is familiar with half-timbered houses inspect it before purchasing. Especially with these buildings, many renovations that look "super stylish" and "really well done" to laypeople ultimately mean the death of the house (moisture / rot problems) due to the use of wrong materials and incorrect techniques.
In any case, with such a house, besides the normal acquisition and incidental costs, you should always plan somewhat more generous maintenance/repair reserves in the monthly cost calculations.

Please also check whether it is a listed building. I would set aside the bonuses as a lump sum for maintenance and rebuild equity as quickly as possible. For the financing, you could compare which interest rate is offered for 10 versus 15 years. If a somewhat noticeable difference can be seen, you can take some risk and put the saved interest into repayment. Security then comes from a low outstanding balance. But this is just a thought; I am far from a financing expert.

Thanks for the answers already,

Regarding the repayment etc,
I can’t manage to pay off the house within 10-15 years, before retirement age it will be a bit earlier (maybe 25 years). I also don’t want to have too high a repayment if I can make special payments (that’s what I thought). 2-2.5% repayment should be enough.
One wants to live, even though I know that now renting
(paying under 500€ for 90m2) I can live more generously without watching every euro.

That will certainly look different with a house.
And I would definitely have an appraiser come if the financial conditions are in place to take a look at it.
I would be interested if you have done this yourselves (full financing) with a normal salary in this range.

I know every house is individual and the buyers are more or less financially well off. For wealthy people who have studied and earn more, they might smile at the whole thing. There are certainly other financial conditions there as well.

I was thinking of a monthly rate between €750-€850 plus additional costs of €250 and €150-€200 for maintenance reserves that I save for repairs. I want to cap that at €15,000 if nothing happens until then. This results in monthly costs around €1,300, leaving a little extra, and even more if I rent out. The other money (allowances, etc.) I would pay into the home savings contract for later refinancing.

After 10 years, the children would be out of the house (estimated), so at least no longer legally obliged to support them, which also means some income will be lost. Although support is obviously available, we are also saving for the children when they turn 18 so they will have some capital later. First apartment, furnishings, car, etc.

My wife would go back to working full-time, so the loss would not be too high but still noticeable.

We are not protected against loss if one is unemployed, sick, etc. I as the main earner would obviously be the breaking point for us.

If I had to go by that, I probably shouldn't do it. But who can say what will be in one year? Residual risk remains, as life goes. If someone loses their ability to work, it is more survival than living, even with rent.

By the way, not a listed building.

Afterwards, in 90% of cases, you are not allowed to leave. Most properties are financed based on a joint income or a main earner. If you fail, the place simply has to go and that's it. It will work out somehow.
A house also has higher additional costs than an apartment. Just make a complete table for yourself. Including one-time costs in the year. For example, I always forgot the motorcycle from time to time.
Then see if you can afford it or want to.
I generally don’t consider a home savings contract to be useful. The costs would be too high for me personally. However, I cannot and do not want to recommend real alternatives. If I were to, I would save the bonuses and make special repayments annually, if possible. But not necessarily factor that in. It’s nice if you can, and not harmful if you can’t.
Also remember that you will have to buy a car at some point, or gifts, or other things. Put everything together realistically.

Personally, I don’t see any problems with 250k at first. The salary and the Düsseldorf Table will increase due to inflation. The debts, on the other hand, are fixed and will be devalued by inflation.
According to a calculator on the internet, the remaining 155k in 15 years at an average inflation rate of 1.5% is still about 124k in today’s value.
And seriously: what are 125k, when you have a renovated property backing you?