Floor plan single-family house SW slope approx. 160 sqm living area + basement

Overall, the property slopes down by about 4m.
It is planned to somewhat balance this slope, probably with several levels.

Oh dear, several levels mean expensive landscaping and earthworks.
However, it is important how the slope behaves within the building envelope.

The slope drops quite linearly towards the southwest, so the house would stand exactly perpendicular to the slope.

That is bad. Usually, it is better to build along with the slope in order to keep the height difference as small as possible.
However, you have to see individually what fits best.

For the access road, a street from the right side of the property is planned (there the right of way applies).
The parking spaces would then be planned perpendicular to the street.

Just draw that out. Preferably on graph paper, hand-sketched with the approximate terrain profile.

Currently, there is no plan regarding the basement. However, the basement should accommodate a guest room, technical room, utility room, shower + toilet.

That is unfortunate and unwise. The basement is the foundation of the house and must carry the rest. Also, you are currently assigning the basement a better position, namely it is the level that connects the house and garden. So let’s not call it basement, but UG, lower floor, because there is living space there.
And now think about it: three levels? The basement is not in the budget. So two levels. Cross out the idea of a “basement” and refer to two levels, the upper level will probably be the entrance, the lower level the connection to the garden.

I don’t quite understand what you mean? The kitchen is directly adjacent to the dining room and therefore easily accessible.

The kitchen and pantry should be reachable on a short route from the entrance area.

The budget is about 650,000

I can link you the last hillside houses discussed here, but you can also search for them yourself.
Here is an example where the entrance is not where the living room/kitchen is
https://www.hausbau-forum.de/threads/grundriss-einfamilienhaus-ca-160m-haupteingang-im-keller-nordhang-1700m.47820/
Here a recognized problem of a slope and considerations about how and which house fits on it
https://www.hausbau-forum.de/threads/grundriss-entwurf-einfamilienhaus-mit-10-suedhang-hauseingang-podesttreppe.49361/
Here a steep slope
https://www.hausbau-forum.de/threads/grundriss-ueberarbeitung-tipps-und-erfahrungen-zur-verbesserung.49467/
Here a hillside construction
https://www.hausbau-forum.de/threads/grundriss-zweifamilienhaus-nebeneinander-am-suedhang.49076/
And also very clearly here
https://www.hausbau-forum.de/threads/grundriss-einfamilienhaus-in-hanglage.49127/
Also has a long thread series with a very good solution 2023/2024, but she seems to have logged off. However, it can be found here.
There are more: just try the search here in the forum.

So if you want to stay within budget, you should set aside an extra 50000€ for the slope ([earthworks, landscaping]). Then another 50000€ for outdoor facilities, garage, and buffer, as well as 50000€ for additional construction costs. You have 500000€ for the house. A good 150/160sqm. To use this well, you should plan about 45sqm for living room/kitchen/dining. 10 for technology, 5 for utility room, 45sqm for 3 bedrooms, and 15 for bathrooms. 20sqm go to stairs and hallway. 10sqm for office/guest. The rest fits in below.

You have €500,000 for the house. A good 150/160 sqm

… and you have to do without the basement. That will be your bitter pill to swallow with that budget.

The unused basement gets the cream slice direct garden access.

Use the basement as a living lower floor. We have that too. Why build a tower pointlessly. The days of oil tanks or coal cellars are over, as are those of storage rooms that get the extended family through the winter

How has the neighbor in the north secured the border? Is there a retaining wall? I did not ask for pictures of the neighboring properties out of boredom. Is it possible to approach from the west? An aerial photo excerpt also helps a bit. In my opinion, a 14% gradient is not without its challenges.

The budget is about 650,000

uh oh, that’s not going to work.

We are currently building on a hillside of similar size, however with a simpler building structure, a lot of own labor and very cheap earthworks (relatives), and we have the same budget.