It's not like a player has to sign an NLI at all; Sabrina Ionescu basically waited until the summer after her senior year of high school and just showed up at Oregon shortly before classes were to start; she signed an ASA instead which is for the most part the same type of financial agreement. She had taken her official visits, including the one to Texas, in the Fall.
As for Chavez, no idea of her timetable. She didn't make many unofficial visits her junior year. Since August, she's made 3 official visits to UCLA, Texas, and OU, with a speculated official visit to Texas Tech yet to come; no rumors of a visit to South Carolina as of yet.
If she or her family really were "shopping around" I would have expected a lot more unofficial and official visits; but, that hasn't been the case. For Texas, I'm not sure if it lowers/increases our chances to sign her if she waits until next Spring to make a decision. To me, her not signing in November could be to make sure Coach Gerlich is retained and gets a contract extension; and, that decision won't happen until the season concludes next March.