Is the total budget for the construction project realistic?

No, it doesn't matter, just pure curiosity. I'm just wondering where in the Karlsruhe surrounding area you pay >500€/m². As for the building plot, what should be disadvantageous about it? We can currently only dream of such a building plot.

I have to admit that the term Karlsruhe Umland is somewhat broad. We mean more the areas close to the city with very good connection to the public transport network and the rest of the infrastructure.

Does anyone else have opinions on the building plot I sketched and its potential for construction? It should be quite possible to build with some flexibility even with a garage and to make good use of the favorable orientation for the outdoor areas, right?

At first glance, it looks like the garage would be perfect there. That's true. But the further you place the garage into the back garden area, the less garden space you have left. That's the Jill area, the pool area, sunbathing spot, strawberry patch zone, rose experiment breeding spot, terrace construction test track, cat or dog petting zone, etc. - if you know what I mean.
A concrete block back there is just a concrete block instead of grass. I think the block would be less disturbing closer to the street.

At first glance, it looks like the garage would be perfect there. That's true. But the further you place the garage towards the back garden area, the less garden space you have left. That is the Jill area, the pool area, sunbathing spot, strawberry bed zone, rose experiment breeding area, terrace construction test track, cat or dog petting zone, etc. – if you understand. A concrete block back there is just a concrete block instead of grass. I think the block would be less disturbing closer to the street.

Yes, sure. But it doesn’t have to be a 9-meter monster garage. On the other side towards the street facing SW, there is (I haven’t drawn it in) another optional area for a garage along the whole side. Here, exceptionally, a garage may be built outside the building window. However, I thought it would be smart to use this side for the living and dining rooms because of the good orientation?

The building envelope fits, a house with a good orientation has plenty of space there. I see the garage currently in the east, but we have to see how the whole design turns out. I wouldn't get impatient now, but in your place I would put a few sketches in a feasible house shape into the window. Then you'll get a rough idea. There are much worse and smaller building envelopes.

Is it not allowed "as an exception" to erect an outbuilding outside the building area on every side? Sorry if you already mentioned this - is it explicitly stated with you that outbuildings are not or only allowed on one side as edge development?