OU was probably the one leading the SEC move initially. OU's Tier 3 deal is the one that was up so they had the reason to start the rights talks. OU was pissed at its old Tier 3 partner, FOX, over the constant 11 a.m. kickoffs. Castiglione took a public shot at FOX when the '21 OU-NU kickoff time was announced. OU had basically begged FOX behind the scenes not to choose that game for "Big Noon" or to kick it later, due to the alumni events associated with the 50th anniversary of the "Game of the Century." FOX told OU to pound sand. That was just the latest in a long list of OU grievance over that issue. "Big Noon" did not exist when OU signed its deal with the Big 12, so the Big 12 and the media side were disingenuous when they kept slamming OU with the "you signed the deal" stuff. I'd guess that when OU approached ESPN about Tier 3, the topic of switching leagues came up with it. From there, OU calls UT and the two start making plans. The SEC was the move that made the most sense, both for the recruiting benefits that would come with it, and the ease it would present for folding the LHN into the SECN. I'm sure UT and OU both wanted to be in the room while the SEC hashed out its own NIL policy.
OSU didn't pitch a big fit in the legislature b/c the Big 12 was given assurances by the media partners about its future pretty quickly, and before the situation could devolve in that direction. ESPN/FOX both signed off on the 4 team expansion. I assume that the 4 team expansion was done with some preliminary discussions over the terms of the next rights agreement, too.
All in all, this is going to end up a great outcome for everyone. A few Big 12 schools are going to win at a higher level than they ever have, play in better TV windows than they ever have, etc., while still making really good money. UT and OU will be in a conference of peer athletic departments for the first time, ticket values will go up, donations will go up, etc.