Alignment of house and garage on the property

You do not understand it currently because you are disturbing yourself with your 10 x 10 house: your building volume with 10 x 10 at the very back creates a long driveway. If you build an elongated building volume, you have a west garden and a shorter driveway.

Well, difficult situation when the plot has no pitfalls and you therefore have the agony of choice! Here in the forum, "unnecessary" floor square meters are often discussed. Here you have wasted relatively a lot of plot with "unnecessary" driveway square meters. If this is supposed to count as a "property" and you perhaps want to hide your celebrity status a bit - okay. But for a simple single-family house, I would classically place the main entrance and garage "in the front." If sunlight is so important to you, then take a look online at the sun paths and shadow patterns. If necessary, you can "optimize" the house volume/roof shape and garage so that the sun can be enjoyed at different times of day and year in great individual spots (e.g. roof terrace on the garage).

I will try a 9x11 or 8x12 rectangle on the property and see how it looks. We generally don’t find the style of the “[Anwesens]” bad. It just resulted from our lack of creativity and by no means to justify an absolutely non-existent celebrity status. “[Anwesen]” is certainly too much said here, for an approx. 160 sqm city villa ;) Our problem is “simply” that with the arrangement “garage next to the house” I also build a long side of about 16m at the front on the south side of the property with the 8x12 rectangle (at about 2m distance between house and garage), which corresponds to about half the width of the property and I’m afraid of too much “north” instead of “west” garden here. Although depending on the sun’s course I should have sunlight in most corners of the garden from the afternoon onwards at the latest (when the sun passes the house). I’m really grateful for your general advice, I’m currently just having a hard time visualizing it and consequently even harder to explain it to my wife… ;)

Here on this street, half of the properties have a south orientation. South-facing terraces are rare and not used, showcase pieces and such. The houses stand close to the street and the garden behind the house is used, mostly a shaded terrace and another seating area with sun. There is a house like you plan, ultra-modern, almost 70% glass, south garden with high water consumption. Brandenburg has water shortages, how long gardens will still be allowed to be watered, who knows. Open living is like cinema.

Look what I wrote years ago:
https://www.hausbau-forum.de/threads/leitfaden-zur-hausplanung-auf-dem-Grundstück.30891/

Thank you very much for the link and the comments. We tried a bit again last night and have now landed on the option that we will probably plan the house towards 8.75m x 11.75m and place it at the front on the boundary of the building envelope. The garage has also been moved forward accordingly. Drawing in the sun paths has somewhat reassured me here; most of the garden definitely gets enough light from late spring to early autumn. Now we need to adjust our floor plans a bit again, but that should not be a problem.
The only thing we still find "disturbing" is the garage right next to the house (which was already the case before). Maybe we will move it 2 or 3 meters further back so that it does not produce a 7m long and 2m wide tunnel right next to the house, but rather leaves more of this house area open. We both do not find having it directly against the house wall very charming.
In the picture, you can roughly see how we want to approach it now. Thanks again!