How is UConn vs Louisville and UConn vs South Carolina a rivalry when those two matchups has been lopsided! South Carolina only beat them once in 9 tries! Baylor has evened the series at 4-4!
Baylor is always a big game but there really isn't any major history between the programs or higher emotions during the game like we've seen vs Notre Dame and Tennessee. Rutgers in the 2000s was definitely a bigger rival, too.
Regardless of head to head records, rivalries have to have competitive games to be classified as a rivalry IMO. Louisville and SC I wouldn't classify as rivals either, largely due to games not being competitive and a lack of emotion induced by playing the opponent. UCONN has absolutely dominated Louisville aside from one loss in 2019, and the games have never been close or competitive. Same with SC, who despite being a pretty central figure in WBB for 8ish years now, has never been able to compete with UCONN aside from last year's win (which wasn't competitive either).
Neither opponent has had any exciting games which is usually a HUGE element of what makes a rivalry great. Compare that to peak Tennessee/UCONN or Notre Dame/UCONN where the games were usually quite competitive, had a lot riding on them, and were decided down the stretch. Each rivalry has several iconic moments and hyper competitive games that fans readily remember 5/10/20+ years later. That's never been the case for SC/Louisville, or even Stanford for that matter.
To be honest I don't think there really is a great rivalry in women's basketball right now. Tennessee hasn't been relevant in a while and the programs haven't played in 13 years. It was always Pat vs Geno and Tennessee hasnt been a contender ever since Pat left.
Notre Dame also isn't currently relevant or a top 25 team and has a new coach. There are lots of good teams but no marquee games in women's basketball right now that will draw in outside fans.