How much installment can we afford?

As long as the numbers are correct, a payment of €2,500 is easily possible with €6,450 net. Anyone who cannot manage with almost €4,000 net for living expenses for three people in their own home does not have an income problem, but an expense problem.

I can save my own contribution there, I see it exactly the same way :)

this category covers pretty much everything you can imagine. Visits to cafes, technical purchases, bicycles, coffee machines, furniture, dishwashers, theater, hairdresser, subscriptions for Prime & co, and so on and so forth... can this be reduced? Sure. Was that the point? Not at all.

It’s not about reducing something.
Look within yourselves. You don’t have to disclose this here either. But from life experience, it is simply the case that consumption habits do not change out of habit just because you have a loan to pay off. If someone often and regularly goes to the beautician and hairdresser, they will not noticeably reduce it.
The same goes for Prime, Netflix subscribers.

One of the cars is also almost new (16,000 km). The mobility costs would certainly increase with the move towards the countryside and it would be sensible to have a reserve fund for the new purchase (of a used) car! Thanks for the tips regarding this : )

You calculate a reserve fund for a car at 500€. Those who want and are able to manage with a 10-year-old car save less.

the installment also includes the initial equipment for the child, for example.

The initial equipment is something different than ongoing costs for baby food, diapers and the like.

Now to speculate whether our child needs more attention or less or or or... is... speculation! The assumption is: 6,200€

Well, honestly: on the one hand you speculate and juggle with (income) figures that are not even fixed now and here, on the other hand you calculate with current expense figures.
With that, you are deceiving yourselves. Ultimately, the forum doesn’t care how you manage in 2-3 years. You have to make sure you come up with realistic numbers and not calculate with fictitious assumptions. That does you no favors.

If you go by the numbers he presented to us (and that was the request), then a rate of 2,500 EUR definitely doesn't fit. Because just the higher housing costs completely eat up the current savings rate, the mobility costs are set far too low, and so on. I also consider the costs for a child to be underestimated, especially with the first child and in the first years, when you basically buy new shoes almost every month... ... but well... what do I know with 2 children. Just for daycare, 200, 300 EUR per month quickly add up. Ever thought about that? ;)

PS: Whether the 1,000 EUR for "sonstiges" are appropriate or not is something everyone has to decide for themselves. However, he obviously has these tasks at the moment, so they have to be taken into account in the invoice and cannot be downplayed with "that's way too much, it could be much less" ;)

I think €2,500 should be easily doable and if necessary, you can adjust your lifestyle a bit. You certainly don't have to live in poverty. It doesn't help to keep nitpicking that one can live on €4,000 for three people. How the OP lives is none of our business. Of course, one can live very well with that, but we don't know what their priorities are. Maybe they like to take a world trip once a year.

I also consider the costs for a child to be underestimated

If he says that the €1000 was like that also because the initial equipment was included in the last months and that part of the €1000 is simply kept permanently as a flat rate "for children" as a buffer, then that doesn't actually sound so wrong...