Not sure what your budget is, but how about a Pergola? It would look absolutely beautiful, doesn't cost a bomb to install and you could add some fast growing vines, be they flower or grape, or a mixture of both, whip the slabs up, lay a plastic membrane and then whack a couple of tons of peashingle down. To finish it off, I would remove the wall in front of the patio and replace it with some large planters containing box hedging, rosemary, or lavender. A little touch of the continent, right on your backdoor step and you won't even need to go through passport control!

I think the door of the shed attracts the eye much less than the walls of the shed. And the door is darker. I’m just pointing that out because I’ve painted a few fences, pergolas and sheds in my time and the first few times I tried light and out of desperation then went dark and have worked out dark recedes. Plus, rough wood is hard to paint and shows that it’s rough much more obviously than dark. But if you husband is a decorator I bet he can do a great job whatever you pick. :)

I understand what you mean, you want privacy without a heavy structure sapping the light and view. How about a metal canopy? Some pictures below. Of course the best way to make the garden more private is planting. A tree near the bottom will provide screening, but ensure it’s not too near buildings or paths in case of root problems. Planting some shrubs along the perimeter fences will help too.

Agree with Angie. Remove them and maybe gravel around the planting you have and extend the gravel to cover where the flagstones were, with sun loving tough plants such as thyme and creeping rosemary which will spill over and cover your wooden retaining panels. Appreciate you have already bought and planted the cordyline but if they die in winter what about lavendar? Just make sure the gravel is in a complementary colour to your patio.