My son was auto admit to the University of Texas. As discussed, entrance to majors is not guaranteed. He applied CompSci, which is very competitive, and got Turing Scholars honors. I had lots and lots of friends whose children applied engineering to UT, many of them not in the top 7% (8% this year), who were successful. It is holistic. There are lots of horror stories about kids who “should” have gotten in, but my anecdotal observation is that a strong overall student with leadership ECs does stand a good chance. There is absolutely no guarantee though, and you should understand that going in.
Texas A&M is switching this year to a holistic review for engineering only. For A&M, you should strive to meet the auto admit stats (they do not take that many out of their auto admit pool), but you can be in the top 25% and still meet the SAT requirements. University of Houston (which is okay, better in Mech E and Electrical) wants to see a score of 600 on the math SAT. Texas Tech is a good option, as is UT-Dallas and even UTEP.
Finally, the state schools do not meet full need, so we found that on average for a strong student with merit potential, a school like Colorado School of Mines ends up being fairly comparable financially. Other students I know are doing engineering at OSU or other neighboring state schools.
Oh and about Katy, it’s former prairie, so it has a certain (very flat) look to it. Everyone says schools are good. I can comment more on HISD and SBISD and somewhat on FBISD.