Schools collectives do offer contracts to the players. We heard recently of he $5 million offer to a QB to transfer from one school to another. Do you think Coca Cola or Academy Sports made the offer to the QB? Why would Coca Cola care about which school an athlete plays? No, it was the Coach of the school that made the offer.
Private companies can make an NIL deal with players, but in most cases school collectives do deals with funds collected from boosters. And they are not thinking of marketing products from their name/image/likeness. They are paying to play. Some coaches are stating this openly. There are school collectives out there that pay each player on the team $10k - $15k per year. Mississippi State payed their 6 top defensive linemen as a collective just to stay on the team and not hit the portal. When MSU would not fork over the amount RaRa was demanding, he transferred to Georgia.
SEC Collectives Ranked: https://www.si.com/college/auburn/football/college-football-ranking-the-strength-of-every-nil-collective-in-the-sec-football