What can we afford? Young family homeownership. (Bavaria)

Depends on how big the children's rooms are supposed to be...

here you don't have to

... 120 m2 for a future 5 people

in my opinion, you don't have to join the megalomania if money is tight.
Smartly furnished and well laid out, that is completely sufficient.

But thinking about it, with just under 3k € net income, I'm actually not a bad earner... Really shocking that as a middle-class person you can't afford a "normal" house

No, that's really not wrong. Unfortunately, land and construction costs have become so high that families realistically simply need two incomes. Together maybe just under 160% of an average income. With 4500€, the calculation would look completely different. So save, activate a second income and then see, or rent a house and start when the children are a bit older.

What do you do for a living? Specialist nurse in psychiatry

I hope you have not added shift allowances to your salary.

But thinking about it, with just under €3k net, I'm actually not a bad earner... Really shocking that as a middle-class person you can't afford a "normal" house...

As a single yes, as a sole earner with 2-3 children no.

Now this won’t work. Start saving, get through the toddler years, and then, with the woman having a part-time job, it will work out for you too.

Somehow the 2900,- net at your age and profession also makes me a bit suspicious...