Is buying a house sensible in the current market situation?!

And when you really have to approach it energetically (that will definitely still come for 2023, 2024), I don't know if the DIY work is still feasible to that extent (underfloor heating, insulation, etc) -

These are exactly the trades where a lot of DIY work is possible: insulating the basement ceiling = 100% DIY easily doable, insulating the roof / upper floor ceiling = 100% DIY easily doable, underfloor heating = laying insulation on a concrete floor and installing underfloor heating pipes is ideal for DIY work (and foolproof, since many heating engineers even take over the warranty for the entire underfloor heating system).
Facade insulation is already more demanding.

We have looked at many things over the last 3 years and thought in all directions (heritable lease, rent-to-own, sharpening blades, writing letters, etc.)

Did you implement it that way too? Did you really drop letters expressing purchase interest everywhere? What is the response like for something like that? Yesterday I saw a new flyer made by children again at the supermarket, where a family is looking for a house. There were even two little notes torn off with the phone number. Question: How many children do you actually have already that you need at least 5 rooms?

These are, for example, trades where a lot of EL is really possible: insulating the basement ceiling = 100% EL easily doable, insulating the roof / upper floor ceiling = 100% EL easily doable, underfloor heating = laying insulation on a concrete floor and installing underfloor heating pipes is ideal for own work (and foolproof, since many heating engineers even take the warranty for the entire underfloor heating system).
Facade insulation is then more demanding.

I see it the same way. Apart from facade insulation, roof covering, and electrical work, you can do quite a bit yourself. Although you can also prepare the electrical work. In the end, it’s always a matter of time and skill.

...and a matter of willingness to provide that. On average, we have become extremely comfortable and are often no longer willing to make sacrifices. I think that will change in the next few years.

Did you implement it like that, too? Did you really drop letters expressing purchase interest everywhere? What is the response like for something like that?
Just yesterday, I saw a new handmade notice by children in the supermarket again, where a family is looking for a house. There were even two little notes torn off with the phone number.

Question: How many children do you actually have that you need at least 5 rooms?

We implemented it that way and still do it (about 80 letters and 10 personal presentations). The response rate (we keep statistics on this, i.e., we write down where, who, and what responded) is, in my opinion, good. We get feedback in about 2 out of 10 inquiries (regardless of whether by letter or personal conversation). It became concrete with 3 properties, but in the end, we were unlucky (the community of heirs did not agree, so the property went to the real estate agent).

We have a toddler and a baby (Yes, it would also work in our current apartment, but we need an office and having a room for each child would be nice during adolescence : ) )

Interesting, I wouldn't have thought you'd get so much response.

The property then went to the real estate agent

Then you could still have bought it. How far apart were the price expectations?