Ok so the issue is where the higher garage founds meets the lower house. The ground must slope down to the house in this area so you also need to think about drainage and the visuals. You don't want to be looking at exposed concrete.
I would expect a standard stepped foundation a few feet along the garage wall away from the house depending on how the ground rises. Some engineered bricks might be needed where partly burried?
Check ground levels carefully to avoid the wall of the house accidentally becoming a retaining wall.
I agree an SE needed to design how the garage floor slab abuts the house.