The strip next to the west side appears so narrow that no meaningful terrace can/could be built there anyway, which is also shaded by the neighboring buildings.
Why does a terrace always have to be attached to the house? Why not a large pavilion-like seating area with a built-in grill and a trellis for a grapevine, etc. at the back of the garden? A curved path leads from the house to the seating area, that would be great!
PS. I am also a north garden builder^^ but voluntarily, because south would have been the street, north is a field... so house to the south and garden to the north... If your house was designed with height in mind, you can calculate the shadow cast at any time of day and year online and see how much garden remains sunny.