Floor plan design for extension of 1970s bungalow - no additional storey desired

I would also deal with how to practically carry that out or implement it afterwards.

Thanks for the food for thought, definitely important. However, I had planned to keep the existing structure (except for the kitchen) as it is. We could then live here more or less "normally" during the extension.

That's fine!
But it doesn't apply to me, since I also spend my time on sketches. And there I have to weigh things up and reject pipe dreams.
I also have no desire for endless discussions and brainstorming that are only based on assumptions (just because the questioner doesn't answer follow-up questions).
And apparently, we don't only have a budget limit here, but also obviously the limit of the floor area ratio.
But an exchange simply doesn't work like this.

I didn't want to keep anyone waiting here and apologize. I really appreciate the exchange!

The budget is 200,000 €. From other projects, I can say that with this amount an extension of up to 100 m2 is possible since we also do a lot of the work ourselves.
I am calculating with approximately 200 m2 floor area ratio that we are allowed to build. I would like to provide a more precise number, but this is not possible so far.

The private green space is shown on the development plan; when I asked the municipality whether better documents and exact figures could be provided so that I could calculate the floor area ratio exactly, I was only sent the development plan. From the neighborhood, I know that it basically works like "the mayor just takes a ruler and pencil and that’s that." In this case, I am definitely on the safe side with 200 m2.

If the plot and the location are ideal, then an extension is also worthwhile, even if it is somewhat compromised and costs a bit more.

The extension variant 1 makes the house an interesting building with a special atmosphere. A material counterpoint could look good. I would prefer this concept to any newly built, no matter how practical, city villa.

It is actually about the fact that we would like to stay here. We have our own orchard at the end of the property and the location is simply fitting. Plots in our surrounding area do not suit our daily life. A tractor in front of the door would make all children’s eyes sparkle in a new development area, and all the adults would be annoyed by the noise. You don’t have to create problems for yourself. Moreover, the price per square meter for a plot is €245. That’s simply out of the question for me. €196,000 for a plot + €400,000 for the house and incidental costs just doesn’t work for me.

Thanks for your last sentence. That’s exactly what I am looking for. Form follows function, but I still don’t want to lose the special something. You can create such great houses from existing properties. Maybe I’m being too narrow-minded, but my dream house is not a Viebrockhaus Maxime 300. (This is not an attack on all Maxime owners, but my personal wish.) And that’s why I am trying to get everything out of this property.

Form follows function, but I still don’t want to lose the special touch.
You can create such wonderful houses from existing properties. Maybe I’m being too narrow-minded here, but my dream house is not a Maxime 300.

If you actually implement FFF and don’t just build random blocks, something special emerges. The special feature alongside FFF can then be a huge window front to the garden, a central fireplace spot, or something else. Of course, such an extension will also bring restrictions, which you might not have or would have differently in a new build, but that is exactly the challenge: to sensibly combine the existing with the new. I have seen so many such projects, and fundamentally that has a very special appeal for me, especially when both wings after the conversion are still recognizable as independent buildings, but are now merged.
Since you are looking for something special, I am missing, in my opinion, the necessary additional detailed information about what exactly you want. A typical single-family house with a pitched roof within a limited budget can usually be planned quite quickly, but a special property cannot.
I probably wouldn’t like it if the new building volume is essentially just extended and therefore cannot appear independent; I don’t read anything detailed about how exactly you want to live or what is particularly important to you.
In such a case, I can well imagine that you might consult an innovative, possibly young architect or even interior architect, because merely generating rooms is too little for such a project. Exactly then you end up with the model XY you mentioned. The variation outside can be reflected inside just as much..... the desired “special” therefore must be clarified in advance, and by that I don’t mean whether it’s a fireplace or wide sliding door, but YOUR truly individually special living style.
Maybe you could show a few examples or descriptions (no links) of what the “special” could be for you.

Am I creating just one construction site at the back or two?

My preferred connection between "building on the front" and "building on the back" would be clearly OR instead of AND. Anesthesia, stopping bleeding, etc.: double operation = tenfold risk. You only do that when you have the devil firmly in hand.

Get yourself an architect and tell them about this discussion only after they have presented their preliminary draft.

I am expecting about 200 m2 floor area ratio that we are allowed to build

Exactly. And 124 sqm are already built on (if you don’t count the terrace). You are left with 75 sqm including outer walls. That means you can generate about 60 sqm more living space. Maybe even 64 sqm. Without indoor terrace. A sentence like

but I don’t really know what to do with the room behind in that regard.

you can therefore save yourself. What you have drawn there in V2 or V3 is already as generous as the existing house.

Get yourself an architect and tell him about this discussion only after he has presented his preliminary draft.

I can only advise you to do so.