Hello, we have a small plot of land in the chaparral desert in Baja California that we're working on, it may be similar to your climate plus we have a lot of mesquite also. We have really sandy soil, above 35 C in summer and bursts of strong wind throughout the whole year and a lot of hungry critters (especially moles) that will eat up whatever you plant and we get 9 inches of rain a year. Also I'm working with a shoestring budget, I don't have a pickup to take large things there. So basically, we've had to make due with what we have and have taken a lot of time to look at the land and wildlife.
After a lot of trial and error, I've decided to work small (like 200 square meters) by working on a flat spot of land, using fencing buried at least 1 foot deep and putting up a physical wind break to deal with the biggest issues: moles, cows and nasty wind gusts that break and dry up plants and trees. I do have an advantage here though, there is some grass (doesn't look native according to my biologist wife) that has taken over flat sandy spots and I will be working with that to build fertility, I think that wherever I want to plant crops I'll add compost from home and smother the grasses with cardboard plus drip irrigation.
I really liked the native grass suggestions that others have mentioned plus rain water catchment. I can also suggest big rocks or structures similar to them, we have TONS of them (literally) and I've noticed that the majority of the native trees and shrubs grow close to them, can imagine it's because they condense small amounts of atmospheric water that keeps them thriving plus the microclimate they help create.
Also, someone was probably referring to the Groasis Waterboxx, it's a great tool for helping trees get established but in my case it's a bit expensive so I would also recommend some homemade wick irrigation containers. I tried them and they helped keep trees alive in 35 C heat throughout the summer, used like around 500 ml per week for every tree planted since I used small containers.
I'd recommend starting with some good nitrogen fixers as well; why not try a different variety of mesquite? The ones we have here are Honey Mesquite: they dont have as many thorns, they attract pollinators, they provide some shade and we've made things from the bean pods. I actually love them, I think they're beautiful. I've also started propagating Leucaena Leucocephala from a local tree that someone planted a while ago, it's one of Geoff's most used trees and from what I can see they'll probably grow great and with very little irrigation. A tree that worked for us is Acacia Saligna, it's a really hardy tree that we started with wick irrigation that we forgot about that just kept growing throughout the summer. These provide very good shade! I also want to get started planting some moringa but I find that these are not as hardy when younger and need protection from the wind, theyre very vulnerable to the cold.