With sovereign immunity - it's that the state can't do wrong and that entering into a contract does not automatically waive sovereign immunity. Most other states have waived this for contract disputes but Texas has not. When Leach was fired, he tried to sue TTU and ran up against that you can't sue the state for damages related to breach of contract. He tried to appeal up to the Texas Supreme Court and they didn't hear the case. When A&M left and Baylor threatened to sue, it was widely thought based on the the Leach/Tech case that they would not be able to get damages from A&M for breach.
The threat is then that Texas could tell the Big 12, "we're out tomorrow and we ain't paying shit" and be in obvious breach of contract but the Big 12 nor any schools could be able to sue them for damages as they could claim sovereign immunity.
And yes, if they say we're leaving but only in 2025 when the grant of rights ends then there is no buyout as there is no contract to buyout from and no media rights to forfeit for the next 2 years.