Franky, with the slope, I might perhaps move a bit away from a "conventional" floor plan. Since it is quite a steep slope, split-level is probably not the choice of things (but maybe you can take a look at matte's house here, for me that's a brilliant split-level solution). Still, it can be utilized. Without further specifications, a basic idea comes to mind:
Very schematic: two levels, shifted against each other. If I understand correctly, the lower level has to disappear quite deep into the ground (here the terrain profile is shown by the red line) to comply with the development plan; possibly it needs to be built more into the ground on the sides, so only windows in the front. The advantages are that probably not so much earthwork is needed and you have an incredible terrace on top and still get sun downstairs (with a balcony it tends to be dark underneath). From the street side, you only see one level. The whole thing can look modern with a flat or shed roof (does the development plan allow that?) or, as I understand, preferably conventional with you, also with a gable or hip roof on top. If done cleverly, you can go directly from the large terrace into the garden if the lower block goes a bit deeper into the ground.
Just a thought prompt, without suggestions on how to arrange the rooms etc. But this way, in my opinion, the plot would be optimally used without forcing a house that was planned for a flat site, with gymnastics that only end in poor compromises, onto a strongly sloped site.
