How much sun does the property typically get? If you want to keep that tree, and you dont get more than like 4-5 hours or so, you might have to just go heavy on shade-loving plants. What kind of tree is that in the center?
For building the soil I would recommend picking up waste organic matter from your neighbors (leaves, branches,
wood(untreated), logs, clippings, etc.). You'd be surprised how much good mulch gets picked up by the
city trash in urban/suburban lawn communities. Just pile it all up, heavier goes on the bottom. Thats hugelkulture!

It breaks down, you get little bugs, microbes, fungi, soil retains more water and good for plants in longterm.
“Sitting at our back doorsteps, all we need to live a good life lies about us. Sun, wind, people, buildings, stones, sea, birds and plants surround us. Cooperation with all these things brings harmony, opposition to them brings disaster and chaos.”
― Bill Mollison