Is our new building realistically financeable?

Let's put it this way, the bank would most likely lend you the money. But I'm not sure if you are ready to make the necessary repayments to pay off the 600k€ in 24 years. Don't forget, in addition to the installment, there are also 400€ monthly additional costs. And I agree with , I see at least a 2500€ installment coming your way to be finished within 24 years. That means you would have 2900€ just for the house. I don't think you want that.

"I didn't quite understand what is going on with the apartment back home.
Of course, that would drastically change the situation."
- in 2017 - last year we bought an apartment at home (new build - stage payment) for about 240K euros. It is fully self-financed and therefore debt-free (we are actually completely debt-free hence the idea of building a house at all). From April it generates 350 euros cold rent but we need the money for parents/parents-in-law, annual trips home, etc. and therefore do not want to consider the 350 as income. But at the moment we pay for all that from our budget here, which would also cease.

Yes, theoretically I could work more but without family etc., 21 hours with a small child is "pure stress". Building a house is still a choice/option and I want to plan with the current cards where more hours are not planned/desired at least until the child is out of elementary school.

And yes, the bank would go along with it (from the first conversation) but mainly because of age I had doubts whether it would be too much for us in the long run.

So if I were you, I would leave out the basement. Saves at least 50k.
With the one child, 140sqm should be enough.

Then I would calculate at least 30k of the 50k, that way the loan amount will be 20k lower again.

The trip back home could also replace another vacation sometimes, right?
So you could finance the vacation with the rental income from the apartment.
Does someone from your family live in the apartment?

And in 10 years you can work more again, which should ease the situation.

So if you can’t build with over 6k and such an affordable plot, then I don’t know either.
But whether you want to pay 2500€ monthly for the installment plus additional costs, of course only you can decide.

First, increase the rent of the apartment. It's way too cheap for a 240k investment.

If you already had the initial consultation: what monthly rate did the bank offer you?

Unfortunately, in your good financial overview, you switch back and forth between monthly expenses and annual savings/performance balance.
That makes it a bit tiring to keep track.
How much do you now have monthly left after deducting all costs including the proportional savings for vacation etc.?

in Heimat eine Wohnung ca. 240K euro selbst finanziert deshalb Kassen leer. Mieteinnahmen ab diesen Monat ca. 350 p.m.

I don’t understand that either. The purchase price corresponds to almost 60 years of rent.