Look at Brazil--herd immunity wasn't enough to prevent another surge. Why should Texas be any different?
The two are not at all comparable. The level of natural immunity is lower, even if we give some wiggle room for likely lower testing rates in Brazil. Brazil has ~5% of the population as confirmed cases, Texas has ~9%. And Brazil is way behind on vaccinations too. In Brazil less than 4% of the population has received at least one shot, while in Texas that figure is >15%.
So yes, I do not see major surges happening anywhere in US, including Texas. Minor surges are possible of course, but I think overall trajectory will be down regardless.