Different kinds of birds like different habits. Birds don't really have homes and this time of year in N Texas I don't think any would be nesting. No "trumpet vine" I know of provides much in the way of food, just some insects. But many plants are called "trumpet vine". I wouldn't be overly concerned as I assume the bramble is just providing shelter from predators. I assume the birds can find suitable shelter elsewhere. Normally shelter isn't a limiting factor in N Texas, it's food, then water.
If you wanted to build a habit specifically for birds you should first determine what kinds of birds. Insect, seed, or nectar eaters for example. Then figure out the limiting factor for those birds, like food in winter, or water in summer, and provide that resource to get them thru the hardest times. There are a very few kinds of birds that have limiting nest sites, owls, wood ducks, wood peckers, etc . For the most part building a habit for nesting is for attracting birds more than increasing overall numbers.
Consider whether what you build could be an ambush site for cats. In urban settings
pet cats and
feral cats are a huge killer of birds and can almost wipe out local populations. So for example if you provide a watering and bathing spot you want no cover for maybe 4-6' around the water. I think woody bush type plants near the water with lots of branches, but no leaves gives birds a place to perch to look for cats and the branches make it hard for birds like hawks from swooping in. Also can make it hard for cats to pounce.
There are lots of
backyard habitat groups that provide info. While they'll a good source you still have to be skeptical. Info can be way over hyped or just plain bad. These are very well meaning people but many are untrained at all and not aware of what's true and what's not.
I think in dry climates like N Texas a pond is about the best thing you can do for birds as long as it isn't a cat ambush site.
Here's a pond I built for birds. It wasn't a huge benefit for watering in summer since San Jose generally had plenty of urban water for birds, it did seem to be a benefit in winter for bathing which can improve bird health. Huge flocks of wintering robins for example would use the pond, maybe 20-30 birds at a time and it would take several hours for the entire flock to cycle thru. Kind of amazingly they never seemed to make a mess at all. Other birds also used the pond including hummingbirds which perched on the edge of the waterfall to bath and they also drank from the falls.