I spent over $4500 for two drought tolerant yards. My requirement was having a reversible yard that can go back to a watered traditional garden.
Weed barrier, top soil mixture of chicken manure, wooden chips. Drip system with timer, solar rain monitor. That includes clean up and rotor tilling etc. I also added some colored pavers to make the yard less depend on water.
Here in Santa Clara County I applied for a grant. While the rotor tilling, laying the drip system and materials cost over $3500. I ordered 2.5 tons of gravel with barrier over and lost 8 lbs on the project.
As for grass, you need to loosen the soil, new compost, top soil mix. I would sprinkle water wise grass seeds now while the ground is wet. A bag of KY low water seeds will do. My sod was just a few bucks. They look fine.
I am a DIY and any gardener knows how to do it. Budget can be over 5K.... depends.
Sam Shueh Realtor