Rather than attempt to screen the entire garden, find the specific spots you will spend most of your time out there, and plant appropriate trees directly in the sight line between you and the overlooking window. That way you can achieve a sense of privacy without it becoming oppressive. The space cries out for deep borders at the back that reflect the curves of the retaining wall. Shrubs with attractive silhouettes will make the best use of that white rendered wall, and dark / purplish foliage would be effective. Multistems would be ideal.
"What is hateful to you, do not do to your neighbour".
I agree with @Loxley idea of selective screening with a small/medium tree. You could also use bleached trees (1st pic, portuguese laurel) or you might even get away with just cylindrically trimmed tall hedges (2nd pic).
BTW Portuguese laurel is much better behaved than cherry laurel.
The reason I think multi stem trees would work particularly well is that the form of the stems look particularly attractive against a backdrop such as a wall, especially if they have attractive bark. They become a sculptural feature in their own right rather than merely functioning as screens. The canopy above will help screen the windows. I don't think dense evergreens would look quite as attractive, and we spend most of our time out in the garden during the summer months anyway.
"What is hateful to you, do not do to your neighbour".
If funds allow I would upgrade the shed, maybe along the lines of a modern style summer house with storage. If not refurbish what you already have - paint, new windows and roof. Specimen trees strategically placed for privacy rather than hedges, I think palms would be good. A curvy path from the top of the steps towards the shed dividing the garden in two. Path could be large pavers with thyme planted in between. I'd go full on tropical
I agree with @Loxley idea of selective screening with a small/medium tree. You could also use bleached trees (1st pic, portuguese laurel) or you might even get away with just cylindrically trimmed tall hedges (2nd pic).
Not sure what bleached trees would look like---probably very ill-looking. Obviously you meant pleached trees. Those can look splendid and effective for screening, but quite expensive.
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BTW Portuguese laurel is much better behaved than cherry laurel.
Joe savage landscape
If not refurbish what you already have - paint, new windows and roof.
Specimen trees strategically placed for privacy rather than hedges, I think palms would be good.
A curvy path from the top of the steps towards the shed dividing the garden in two. Path could be large pavers with thyme planted in between.
I'd go full on tropical