Financing private real estate purchase

I also find that too tight. With your imaginary rate, you are higher than your warm rent. In addition, the monthly ancillary costs come on top.
Furthermore

Mobility costs:

[*]Insurance 90€
[*]Taxes 30€
[*]Fuel 200€

.. the savings rate for the next car as well as repairs, maintenance, inspection are missing here.
For the latter, you have to reckon a flat rate of 50-100€, if you calculate 600€ for an inspection plus new tires or brakes every few years.

Leisure and others 700€

Phone, internet, mobile 80€

Care/drugstore/medicine 200€

Wow, wow, wow, I find that insanely high. It may be normal costs if you don’t have to do the math, but in my opinion, that’s where you have to start.

Definitely get yourself a household budget book and see where your money goes.
With 4400€, financing of almost 400,000€ is too high if the costs are not under control. Everything is not getting cheaper, and you should counteract consumption a bit.

especially since with your own house, the desires also increase. You just want to have more. a lounge seating group for the terrace, a grill, maybe a fireplace, a small garden pool, plants, lawn mower, etc.

If you then only have 5k emergency money left and are drooling in the hardware store and maybe still have to cancel the vacation, then you really have no joy in the house.

The money is then gone very, very quickly.

Stick to it. It’s not enough, especially not if another child is coming. Where you are moving to, to the outskirts, you also need 2 cars. In the end, you don’t even have the money in the account to pay cash for a new washing machine...

You just want to have more.

... not necessarily more. But it’s true, you want to nicely and freshly furnish the new terrace or the added room. Curtains no longer fit. Moreover, the reality is that when you renovate and move, quite a few electrical appliances suffer. Especially the white appliances due to transport, or the vacuum cleaner, because renovation debris clogged it up.
Furniture also no longer holds up to what it promises, etc. There is no buffer for anything.

What are your further plans? Will the woman be working more again in the foreseeable future? If yes, I would dare it. Because then it is a foreseeable period in which the belt has to be tightened a bit. A few years will do with used furniture, the vacation in the own garden, the kids also don’t have expensive hobbies yet, and you avoid the hardware store. If you really want it. Then there is no frustration that you have to restrict yourself a bit.