Whether the 9 m span works is determined by the structural engineering. For our garage, it worked; for the house in the basement for me, it says the ground floor required beams at much less than 9 m.
The budget does not match the house. My tip is to find someone who plans the basement and ground floor together, including execution. When I think about how often the architect was on our construction site, sometimes even with the construction company and the structural engineer – never separately.
Do not underestimate the outdoor area. As you have drawn it, you need a six-figure amount for retaining, removing, and filling.