The yard will serve several interests and one of those will surely turn out to be VIEW. If too much of the yard turns out to be flat or hard-edged, man made materials, it might fall short of becoming the view it could have otherwise been. Consider what goes in a planter. Will there be a small tree (such as in your "idea" photo)? If yes, I'd bump out the apex of the "L" in order to make it a little roomier ... enough that it might actually support a small tree. Maybe you'd want to make it symmetrical and place another small tree at the opposite far corner of the yard? Maybe you'd want to make the planter be a "U" shape? If access to an alley is needed, be sure to account for that in your plan.

Insofar as under the stairs, much of that space can't accommodate anything that requires a person to stand. Storage is a good option. At any portion above 6'-6" you could place a table, counter or whatever else makes sense. Be sure people can move around without bumping in to the lower portion of the stairs.

I like the wrap for the corners, but since you already have "use" of your neighbor's trees, could you put a large shrub in the corners like a rhododendron or another good for your area? Something that would come up over the top of the fence, but not quite a tree. Your plants that are moving should work well closer to the house.

Can you use the permeable pavers? I think there are ones that use grass inside the paver and ones that just let the water flow through.