Baton Rouge is a majority black city (53.4% black per 2020 census) but you wouldn't know that sticking to the area around the LSU campus. The town is very segregated. The football players and other athletes interact a lot with girls from Southern U (which is also in BR). I'd bet the black population at LSU is probably similar to UT though, at least % wise (bear in mind that UT is twice the size of LSU, and Austin like like 4x the size of BR). I do not care for Baton Rouge whatsoever, having lived there for five years and gone to high school on the LSU campus, but the black football players are pretty damn comfy there. I also do not think Austin wins a "diversity" argument against Baton Rouge. Austin is 6.9% black.
That all being said, I highly doubt that is determinative of him going there at all. It's like the guy asking Bobby Burton on the IT Livestream if the A&M journalism school thing would affect A&M's ability to recruit black players.