Also... the photo with the pink arrow is for reference only. This was from a zillow ad for the house...obviously when it was in pristine condition. It did not look that great when I started shoveling out the grass 😄

Since that tree doesn't look very happy and wouldn't fit in well in a xeriscape I would remove it. You could replace it with a small low water use tree or shrub. Desert Willow ”Art’s Seedless”, Texas Olive, and Mastic tree have stayed small for us. For shrubs a texas ranger like ”Green Cloud”, a tall Prickly Pear, or Totem Cacus would look great and they have spineless ones!

The world needs more trees not less but that one certainly isn’t happy currently. I would rethink weed cloth, usually just leads to more work.