How is a 400k loan financible without equity? Net equity at €4,500

What's really bad is something else... of course, if you can't even get away with the family for a week over the next 5 years because of building a house, then something went wrong with the financial planning, but if you stay at home for a year, so what. Then the kids just have to make do with holiday camps and the parents relax in the beach chair on the new terrace. After all, why put all the money into your private little paradise if, when you finally have time, you end up sitting on some grimy hotel balcony or on a hopelessly overcrowded beach again?

That’s exactly what I find burdensome. Not all the money should flow into the house SO THAT one can (whether alone or as a family) afford financial freedom and some comforts on the side. But that is highly personal. I have never sat on a dingy balcony. But rather in pretty holiday homes. And where is life when you just sit at home for five years? Germany is beautiful, but it quickly costs 400€ if you go away for a long weekend. Sure, hiking is nice and you can do it at home too. BUT it’s also nicer sometimes to be in other regions.
And slowly now: the Baltic and North Sea are by the way NOT cheap. You can fly to Turkey for less money.
But it is nice in winter to see real snow for a week sometime. Or to extend the summer by a week. You don’t need Bali; you can easily spend 2500€ for a week that way. Don’t feel like cooking after a long day? Sure, just sit down and have someone serve you. Or order in. Definitely better than canned ravioli or having to cook forcibly.
All that is quality of life for me personally. Who knows what will happen to me in five years?

That’s exactly what I find burdensome. The whole money shouldn’t just flow into the house SO THAT one can afford financial freedom and some perks on the side (whether alone or as a family). But that’s very personal. I’ve never sat on a dingy balcony. Instead, in pretty holiday homes. And where is the life if you just sit at home for five years? Germany is beautiful, but it quickly costs 400€ if you go away for a long weekend. Sure, hiking is nice and you can do it at home. BUT it’s also nice to be in other regions sometimes.
And slowly now: by the way, the Baltic and North Sea are NOT cheap. You can fly to Turkey for less money.
But it’s nice to see proper snow for a week in winter. Or to extend summer by a week. You don’t need Bali for that, you can easily spend 2500€ for a week just like that. Don’t feel like cooking after a long day? Sure, just sit down and be served. Or order in. Definitely better than canned ravioli or having to cook by force.
All of this is quality of life for me personally. Who knows what will happen to me in five years?

Yes, of course everyone decides that for themselves; thankfully even.
Still, you describe it somewhat dramatically or extremely when you call it a "grimy balcony," "sitting at home for five years," or "canned ravioli" as opposed to a great holiday in Turkey, real snow (does it still exist in Europe?), etc.
Just by probability alone, you’re more likely to encounter a grimy balcony on an all-inclusive holiday or be crammed five to a so-called family room with a side sea view... obscured by the crane of the neighboring construction site.
Of course, that’s also portrayed extremely and when I’m away in distant places more often, I never need the kind of money you mention, and I always have it so nice at home that it’s hard to have it nicer anywhere else.
Therefore, I DON’T HAVE TO travel to have it nice but I CAN if I feel like it. I also DON’T HAVE TO cook, instead I may and want to grill or cook something new together, and honestly, I often have problems nowadays when people say they want to go to a restaurant to finally avoid that hard kitchen work on vacation. We all have dishwashers here and the fanciest tools to really make the work easier. Cooking some spaghetti in the evening or a salad or something else with little effort doesn’t mean real kitchen stress.
But all of this is always very individual, which is why it would be a horror for me to fly with kids on school holidays to a hotel vacation in Turkey or somewhere else; but that’s always a matter of character, and thankfully we’re all different, otherwise there would be as many people at the Northern Lights in Norway as at Ballermann or Waikiki Beach.

Worse things exist... sure, if you can't even take a week off with the family over the next 5 years because of building a house, then something went wrong with the financial planning, but if you stay at home for one year, so what. Then it just has to be the holiday activities for the kids and for the parents to relax in the beach chair on the new terrace. After all, why would you invest all that money into your private little gem if, when you finally have time, you end up sitting on some dingy hotel balcony or on a hopelessly overcrowded beach again?

Please keep in mind that I didn't start with the dingy balcony or with eating out. As a family, we often stay in holiday homes. I also like and often cook myself.
But: If I, for example, like to go to the Harz with the family in winter, then a few hundred euros are gone in no time. Going to the Christmas market here, riding the Brockenbahn for the kids, etc. That adds up. And I do that gladly, just like the kids. Personally, I don't want to give that up for a house.
Also with cooking. Maybe I just don't feel like cooking after 12 hours. Then I order in advance and pick up food. Sometimes spontaneously around 40€. Give that up? No, why? Then I just make compromises on the house.
I bought cheaply 40km away from Hanover. We have an income similar to the OP. But through compromises in terms of location and layout, we paid a total of about 230,000€ including renovation. We find it nice and sufficient. But we wanted to stay financially flexible to enjoy the nice things in life.
We just don’t want to give up the aforementioned things. Others gladly do that for the house. We are not willing to.

Please keep in mind that I neither started with the filthy balcony nor with eating out. As a family, we often stay in holiday homes. I also like cooking very much and often. But: If I want to go to the Harz with the family in winter, for example, then a few hundred euros are gone in no time. Here to the Christmas market, taking the kids on the Brockenbahn, etc. That adds up. And I like doing that just as much as the kids. Personally, I do not want to give that up for a house. The same goes for cooking. Maybe sometimes I just don’t feel like cooking after 12 hours. Then I order ahead and pick up food. Sometimes spontaneously a relaxed 40€. Give that up? Nope, why? Then I make compromises on the house. I bought cheaply about 40km from Hanover. We have a similar income to the OP. But through compromises in location and layout, we only paid about 230,000€ in total including renovation. We find it nice and sufficient. But we wanted to stay financially flexible to enjoy the nice things in life. We just do not want to give up the things mentioned above. Others gladly do that for the house. We are not willing to.