“What I don’t understand is since UT-Austin is a state school, couldn’t the Texas legislature just step in and bar their Affirmative Action policy? And if so, why haven’t they already done so?”
The entirety UT Board of Regents was appointed by Republican governors.
It was the Republican state legislature that passed the 10% rule.
Ironically, the reason for the challenge is the legislature's solution to Affirmative Action without actually banning it:
If you are in the top 10% of your high-school graduating class, you are guaranteed admission to UT Austin. That accounts for about 75% of every freshman class.
It results in heavy competition for the remaining 25% of spots. The UT Board of Regents uses race as one of the criteria.
Frankly, I don't know why the Legislature hasn't just banned it outright, but I suspect it has something to do with the makeup of the TX legislature and rules that prevent a bill from advancing in the Senate without 2/3rd support.