House purchase or new construction - What is financially feasible?

I am surprised in this case that there are supposedly already concrete offers for a 900k loan. To be honest, I lack the imagination in the current environment that a bank would approve that and then at an interest rate of 3%. That is practically a top rate nowadays.

I did not complain, I am fully aware that we live a privileged life.
I can only answer the vacation question when the time comes. But we go away for 3 weeks in summer and one week in spring/fall during the holidays. And over Christmas, we stay home for 30 days. The rest has to be covered by [Ferienlager/Oma/Opa] and my wife's flexitime.
Vacations are essential to me for education. We traveled through Asia with a backpack and public transport, toured the natural wonders of the USA. With the Jeep and roof tent through Africa, by bike through South America. The memories are worth their weight in gold. The next years will be different but equally important vacations, because then I have unrestricted time for the family.

I didn't complain, I am fully aware that we lead a privileged life.

I can only answer the vacation question when the time comes. But we go away for 3 weeks in summer and one week in spring/fall during the holidays. And over Christmas we are also at home for 30 days. The rest has to be covered by holiday camps/grandma/grandpa and my wife's flexitime.

Vacations are essential for me for education. We have traveled through Asia with backpacks and public transport, visited the natural wonders of the USA. With the jeep and rooftop tent through Africa, by bike through South America. The memories are worth their weight in gold. The next few years it will be a different but equally important vacation, because then I will have unlimited time for the family.

With this attitude towards culture and education, you are actually predestined for the city apartment you currently live in. Have you ever considered combining the missing garden with your apartment by leasing cheap allotment garden land? Usually, a neighbor also takes care of your plot a bit during the vacations. And/But yes: you are bound to certain rules there, also to operate a real kitchen garden. But that's education again right away.

I did not complain, I am fully aware that we lead a privileged life.

I did not take it as complaining either, but quite differently, namely actually psychologically. .

Even though of course we have privileged problems, the thought frustrates me that the added value of a house cannot really be justified financially.

. . precisely because limits are shown to you that you did not know before.

have everything

we enjoy the possibilities of life

The current state is seen as privileged, a small own cabin with garden is missing, but suddenly there are limits that did not exist before. For me, that is a psychological problem. But I also don't see you (plural) / you (singular) in a house with a garden that you can't just leave alone for several weeks. If you travel a lot and possibly also for longer periods, then I would not make it a real estate investment. I would do it via garden sharing, allotment garden or whatever is offered there with you. Possibly one can also buy/lease a permanent pitch for outdoor living in the green vicinity. Decommissioned caravans with space are offered again and again.

Not everything can be done at the same time. You always have to make compromises somewhere. In Germany, vacations are also possible where you can do something for education. I once went to Weimar with my family. Bauhaus, Goethe, Schiller and so on. And if you say you would like to have a garden so that the children can learn some craftsmanship, why are 100k planned for landscaping? No personal effort and everything from the best costs, of course. A working hour of a craftsman can be estimated at at least 50 euros. And a house with everything involves very, very many working hours. Either you let everything be done and give up something else or you take fewer vacations and invest your own effort. I have 2700 net and built a city villa with 192 sqm with my own effort for 1300 euros per sqm. Three years of my life went into it. The plot was inherited and I had 150k in equity.

I would also keep the apartment if I were you, especially if private consumption is that important to you. The children don't get any cheaper, and the city also offers more easily accessible activities for teenagers. My wife is currently the chauffeur for the boys and very annoyed to have to play taxi every day.