You need to maximise the space. If this was mine, I’d probably go along the following lines:
Take out all the planters taking up floor space and don’t introduce any new ones.
Cut back any overhanging foliage from neighbours plants.
Freshen up the walls with white paint. I know you say you don’t like the white walls, but they are/can be great for making the space feel brighter. If you really don’t want white, maybe a pale sky blue?
Your idea of a pale stone floor sounds lovely. I would also maybe look into a resin floor - no pointing to keep fresh etc?
To introduce greenery, maybe two sets of shelves running around the walls with small pots on?
An L-shaped sofa type arrangement in the right hand corner. I’d spend a bit of time looking for a table that’s adjustable. You can get ones which can be set to coffee table and dining table height. That way you get maximum use from the seating area.
And an outdoor rug that complements whatever colour scheme you go for.
Rather than money on a garden designer, I’d probably rather pay for an electrician to sort out external plug sockets and lighting - your space could be transformed in the evenings with some strategic lighting.