Estimating shell construction costs for an extension - Who has experience with that?

Yes, I would have done all that myself. Because the question about the roof shape came up. A simple shed roof.

How does it look in terms of approval? Do I first need a drawing of the whole thing and then have it approved? I actually have almost no documents from the rest of the house. Only a few very old ones, some of which are not 100% accurate.

Is that a problem?

My idea would be like this: I go to a carpenter and tell him what I plan and what he should build for me. He makes a drawing, with which I go to the authorities and get it approved. Then the carpenter makes a structural analysis and I first have someone lay the slab. Afterwards, the shell construction with insulation and roof is completed by the carpenter. The window maker installs the windows and doors for me, and I will do the rest comfortably by myself.

No no, you are still quite far from reality. With the mentioned personal contribution, I would estimate around 55-60k. The plans must be submitted by someone authorized to submit building applications, that is an architect or civil engineer. Is the whole thing even eligible for approval?

I think/hope that it is approvable. How do I find out? Should I approach the municipality with my plans? Hm, that is definitely more than I thought. But well, I will only know for sure once I get all the offers.

Go to an architect and have them tell you what it costs. 50k and more for the few m2 with so much EL is very unlikely...

The plans must be submitted by a person authorized to submit building documents, which is an architect or structural engineer.

It does not have to be an architect or structural engineer. A master carpenter is also authorized to submit plans.

The costs before expansion will amount to approximately 50,000. The remainder in EL you can easily manage with 10,000. So in total, you are looking at at least 60,000 euros.