Is a new building realistic?

As written... I also think it is feasible, but would strongly advise being honest with oneself - there won't be much Caribbean vacation for the time being.

So we also get by with 300-400€ for groceries for a 3-person household.

Please remember that you have to live decently and should not have to give up normal things in life because of a house. A nice barbecue evening in summer can easily cost 50 - 100€.

So we also manage with 300-400€ for groceries for a 3-person household.

I really always wonder how people do that. Even when we were still in training, with two people we spent 400-500 EUR. Including a lot of cooking and really a lot of fresh vegetables, fruits, etc.

Now with 2.5 people and daily cooking, it's easily 800-1000 EUR per month. For us, food is somehow a part of quality of life... and no, I'm not 150 kg

800-1000€ for food per month
But that is rather an outlier on the high side.
With 3 people, we also manage with 300-400€/month (where all food is included in the daycare).

I find the household presentation very current, with little foresight.
Could work with frugality.

This is actually not supposed to become a discussion about how much everyone spends on food per month. It was more about the OP thinking about whether his numbers are realistic. He also mentioned "living expenses," which to me includes more than just "food" - so also hygiene products, possibly diapers, detergent, etc... in other words, everything you need for daily use. And 300€ per month is not particularly much for 3 people - but that doesn’t mean it’s not possible... during my student days, I also lived on 150€ per month - it was possible, but it had little to do with healthy eating.

Please remember that you have to live reasonably and should not give up ordinary things in life because of a house. A nice barbecue evening in summer can easily cost 50 - 100€.

Sure, living reasonably is very important, and the 300-400€ really referred to a completely normal month, meaning balanced meals at home without barbecuing, etc. Barbecuing without a garden is difficult anyway since there is no house yet.