Could it be Escallonia bifida? Just swinging wildly here, but I'm sure someone will recognize this one.

I recently planted a group of 'Bombshell' hydrangeas that I purchased in the fall and wintered over in pots. They are really taking off....tons of branching. These hydrangeas are supposed to reach only 36" with white panicle flowers. I can't personally comment on their flowering, but am hopeful for a nice display later in the season. I've seen lots of nice pics of it on the internet, but have also heard mixed results on this board regarding this hydrangea. Time will tell. I'm hopeful.

Any trees big enough to cast shadows as large as you want will 1. Take years to develop to that size 2. Will almost certainly be too big for the available space In fact there is no in-ground space for a tree at all where you have the existing canopy set up. However the climbing plant that is growing from the bed up onto the corner of the house does suggest the alternative solution of putting up a trellis or arbor and furnishing that with a fast growing climber. This approach would have its own issues of course, including a need for effective annual pruning and training, to get the climber to assume and maintain the desired shape. And not damage the downspout or other parts of the house. And the climbing plant dropping litter onto the drive (as trees would do also). And the installation becoming a possible highway for rats up onto the house (as trees planted so close to the house would probably be also).

https://www.target.com/p/spiraea-vanhouttei-1-root-stock-van-zyverden/-/A-53349489?ref=tgt_adv_XS000000&AFID=google_pla_df&CPNG=PLA_Patio+Garden+Shopping&adgroup=SC_Patio+Garden&LID=700000001170770pgs&network=g&device=c&location=9010288&gclid=EAIaIQobChMIotn0heDJ2wIVQkSGCh1D5QnFEAQYAiABEgIrIPD_BwE&gclsrc=aw.ds vanhouttei ?