I lived in San Antonio for 4 years and had a kick ass garden. The house started with an overgrown mess. Landscaping is a multi-year, possibly never ending project.
The light green bushes by your door are a variety of sage. You can cut it back severely and it will regrow. Best done in early spring, but it is an almost indestructible plant.
Remove the rosemary. I suspect it doesn't have enough sun (hard to tell in the photo) and it is mostly dead. A new plant can be put in in the spring. Just get a small $4 one and water well rosemary needs lots of sunlight but will otherwise thrive in San Antonio. Maybe find a better location for it.
Clear out the ugly, the half dead, the invasive, etc and focus of making light and space for the plants you like and want to keep. Take out anything that doesn't have adequate light.
Grass in Texas requires watering to stay green and alive. My first year there I ended up killing my whole,lawn because I thought watering grass was stupid and unnecessary (true in other parts of the country). So that strip along the extension needs water, regularly, and deeply. Maybe once a week with a really good soaking. Also a deep hard raking to remove the dry clumps of grass and loosen the soil.
The green onions are just onion weeds. They grow everywhere and aren't tasty (very woody). I would recommend pulling them out. If you want to grow onions it is easy to do from onion starts in the spring. You need a well turned vegetable bed.
The roses have several problems. First, many of them appear to be in areas that are too shady (because they are txt remedy leggy) and those likely should be cut back and moved or removed in the fall. Others should be severely cut back (to about one foot high) in the early spring.
I hope that helps. Good luck. Not sure what the rain situation is like down there now. We had one extremely dry year (11" for the whole year) and the established plants did fine.