Construction project feasible with financial resources?

I think that without an ELW the construction wouldn't be approved at all.

The OP will be able to explain that to us. I had understood it differently, since he writes:

Thanks for your assessment!
The ELW must demonstrably be rented out for 5 years.
The purchase contract for the building plot states that in case it is not built as agreed, a penalty must be paid....

In my opinion, this door is deliberately kept open by the municipality and against a "fee."

You can build differently than in the building application if you find an architect who makes two plans and doesn't get caught.

I would find aiming for such things completely inappropriate.

If it is planned properly, an ELW is definitely worth it, especially if it is occupied by relatives.

"Worth it" has several perspectives. You are simply no longer alone, you have to pay attention to the needs of this apartment in the planning as well, etc., and put your own needs aside in some places so that it will "pay off" financially in the end. That would never have been my life model but I am not the standard for others.
We built for the two of us with many thoughts about details and our individual needs and wishes. Today we are also glad about that. Even just with children, one has (we also had that in our first attempts back then) "must" put many personal things aside for the good of those, which as a family one also gladly does or which is partly the epitome of family.
But if, as here, there are no children, I would want to focus my home as much as possible on myself and certainly not on strangers as tenants. Relatives don’t give you anything for free, why should they, and the hope that there are no problems in the family has very often proven to be exactly the opposite. I was just visiting someone who in the end even sold his beloved house because of family in the rental apartments.
It can all work out but under no circumstances would I incur such risks unnecessarily.

Unfortunately, I have that fear too.

But that can be easily clarified at the office.
Maybe you just bought the wrong building plot but that can also be changed.

The question then is, what is "right"?

"Right" means something different to everyone. In my first house I had my parents living there and wanted them to live "properly" nicely. They would never have been shoved into a basement apartment. My "right" would mean to create an equally nice ELW, i.e., a nicer floor plan, sunlight, a nice bathroom and kitchen, an apartment where you like to live.

And what capital must be invested for that?

About the same as for the main apartment, why should it be cheaper?

How much more money could we invest for that without making ourselves unhappy?

Also here......everyone has different pain thresholds as to what makes them unhappy.

Relatives will not live there in the foreseeable future.

I would discard this thought right away anyway because it contains no advantages, only unrealistic hopes. Relatives do not have less interest in their own lives with the same wishes and needs. Often there are unfounded expectations in both directions regarding relatives, from the tenant as well as from the landlord.

What exactly does the office say about you wanting to build a house for the two of you there? Have you really asked them concretely?

What exactly does the office say about you wanting to build a house for the two of you there? Did you really inquire about that specifically?

I will ask specifically, admittedly it can be interpreted both ways in the purchase contract. I will get back to you then, thank you all in advance. We have not bought the land yet, so a reversal is still possible. But since this place has been our best chance for 4 years to finally live the way we want (namely with a garden and WITHOUT family underneath us), we don’t want to leave anything untried. The place itself is nice, an unbuildable edge-of-town location.

[*]Total income 5,350 €
[*]Total expenses 4,684 €
[*]Balance 1,766 €

I somehow have a different calculation.

many things are needed twice, like entrance, electricity/water/heating meters, kitchen, bathroom. Garden costs significantly more.

Yes, you can save on that, but an ELW still costs money.
If you then skimp on the balcony, the target group becomes small.

The ELW must be demonstrably rented out for 5 years

And then try to find a tenant who wants to live under your roof. For many, it’s a red flag to share a roof or the driveway with the landlords.
You have to be able to divide 500 sqm well so that the lives of two parties run satisfactorily on the property.

So 23,700 €. We actually don’t want to proceed that way, but it would theoretically be a door.

But it will be the cheapest solution.

But it’s also about the fundamental question for you whether your salary is even enough for a house?!

finally living the way we want (namely with a garden and WITHOUT family below us)

But WITH a stranger above you.

Difficult.

I somehow have a different calculation.

That's true, sorry, something got mixed up there.
Income €5,350
Expenses €4,243
Balance I €1,107
Balance II €3,227 (savings contributions that will be eliminated)

But for you it’s basically about whether your salary is even enough for a house?!

Exactly.

Exactly.

If a house is important to you (whether it is this property or not) then I would calculate differently.

from this total cold rent and dispensable savings contributions (e.g. savings rate for house) 1200 € savings + 100 € vacation + 450 € car + 70 € gym

retirement provision 500 € ETFs

Take your balance, subtract another 200€ for additional ancillary costs (home insurances, garbage, sewage, etc.), then your retirement provision (ETFs), because the house will be your retirement provision, and then of course the savings rate for the house. Yes, it is wise to keep 300€ of the savings rate. However, in the first years there will hardly be any significant costs related to or around the house. Surely, other things will need to be saved for in the first years, such as new lawn mowers, garden furniture, etc. Consider: not all banks finance furniture and kitchen for you. Also, exterior facilities would have to be financed. You will not like the ETFs, but it is ridiculous to ask here WHETHER you can afford a house if you also want to provide twice by building capital elsewhere. Because then I would say: it won’t work. Having or not having 500€ for financing. Your salary is not bad, but at some point you have to decide to make the savings liquid. Building a house is a good time for that. If you die old holding the ETFs still, you have gained nothing from it except looking at numbers.