House purchase or new construction - What is financially feasible?

I have everything except time

Another reason against owning a house.

I have everything except time and therefore we have so far also discarded the allotment garden.

In my opinion, a wrong strategy, possibly due to a flawed way of thinking. The time argument is valid only if the house does not cost more time than the apartment, but the garden comes on top. The house, simply as a residence, will already demand significantly more time than the apartment even before the advantages you are aiming for set in. I assert: this additional time consumption is certainly not less than what you would have with a rental garden (of any kind). Rationally considered. However, buying a house is primarily an emotional matter. That is also okay - but then please do not rationalize excessively.

(...) Therefore the wish for the house with a garden, because we are absolute outdoor people and often only have one hour left during the day. (...)

Then I would forget about that. Either with the house with garden or with the extremely high amount of personal effort to do all the outdoor facilities yourself. In one hour you might manage to keep your garden, which was completely designed by the gardener, in shape, but nothing else. Such an outdoor facility is not something you can get done in half a Saturday. Many, many weekends and several yearly vacations will be gone for it.

On the other hand, you also don’t have the money to have everything done, because 20,000 EUR per year goes on vacations and vacations with older children don’t necessarily get cheaper...

And the payment for a 900,000 EUR loan will certainly be somewhere around 4,000 EUR? That means vacations won’t be that generous anymore anyway.

Can you imagine a city apartment with a garden? The best of both worlds, perhaps?

We had an apartment in the city with a garden for two years - and that was the worst of all worlds. All the neighbors can look into the garden, as soon as you speak louder than whispering, grill, or even have a party, the neighbors go up in arms and the property management lays down rules about the design. We basically only had work, costs, and didn’t want to use the garden.

Especially since that wouldn't be easy to find, because for every 10 multi-family houses with multiple parties in the backyard, there is only one garden. And I also don't imagine it to be very comfortable to always carry everything up and down 2 or 3 floors...

It is what it is. A single-family house with a garden is a nice thing, but it takes time... how much time, unfortunately you only realize once you live in it and no longer have it. And if you don't want to sacrifice the time, it costs money, a lot of money... for the gardener, for the cleaning staff, etc.