There are plants at the south of green house to have more relaxing atmosphere for studying area. For this
purpose, I propose to use the vases you have already bought.
Moreover there is another plant base above the parapet and it is used to separate pv panels. So you will have a private space as you asked for. It is a good idea to use steel cable attached to the structure for your climbing plants.
I did not separate relaxing zone and dinner table. There should be a long L shaped sofa which also serves for dinner table so you may use this space for more crowded groups. Furthermore one shading element would be enough for all guests.
I designed a small kitchen zone which includes barbecue, sink, and cabinets. As I understand from your notes, north side has a nice view. It would be pleasant to work here.