Good morning Tassimat,
we currently rent a single-family house where the ground floor is at the garden level on the upper floor, so the basement is at ground level (hillside location). We are very annoyed that we cannot go directly into the garden but always have to go "through the house," hence the idea with the stairs.
The budget is a good question. The goal is definitely to stay well below the cost of a new build, which hopefully can work. Ideally, it should not cost more than 200,000 euros, including expansion, etc.