From what slope is a basement sensible?

Above all .. garage will then get the south-west side, which is indeed very suitable for regular rooms.

Whether a basement makes sense depends on your needs and not on the topology. A basement can mean an additional bright floor on steeper plots. Our neighbor has bright basement rooms at the front, a ground floor, and an attic with a sloping roof. This way, he was able to accommodate a lot of living space on a compact plot, as only 1.5 stories are allowed. He accesses the ground floor from the street via a staircase. Just because it is "cheaper" than building a basement on flat terrain doesn't mean you have to go for it.

Whether a basement makes sense depends on your needs and not on the topology.

Absolutely yes, relatively (i.e. with a specific plot) not or, but and: because where a plot is concretely located, there is also its topology. And if the topology clearly says "yes" to the basement, one can still have a different opinion - but that is then a stubbornness that costs.

It would be a rational decision to take a basement for cost reasons. Because it is so cheap compared to the fill. However, placing living spaces downstairs is a special matter. Not everyone wants to live in the basement. The rational argument doesn't help with that either.

Putting living spaces below ground level is a special matter. Not everyone wants to live in the basement.

Living spaces do not belong in basements (those that are buried deep on all sides), but at most in lower floors (those that can breathe light without snorkels because they are exposed on the valley side). Therefore, I only recommend basements for utility rooms or at most guest rooms for rare use, or purely fiscal "offices" where you just put down your laptop bag and sit over your tax return.

It would be a rational decision to take a basement for cost reasons. Because it is so cheap compared to embankment.

A basement is not cheaper than an embankment. Rather, I am simply saying: where you practically already build a complete basement in terms of exterior walls, you can also give it a floor and partition walls. Then the strictly speaking unnecessary hobby basement is at least cost-neutral with respect to the excavation and slope stabilization measures when rarely setting up the Carrera track.