Answer: first distinguish between personal labor and monetary enticements.
1. The 13th Amendment to the Constitution forbids enforced peonage. No court will force a person to work or labor when the person doesn't want to. Period ... with the exception of forced labor in prisons, and folks in essential industries who can be forced by the federal government to work rather than go on strike.
2. When a person signs a contract promising to work and then breaks that contract to work at a competitor, a court may, by injunction--and depending on the terms of the contract (non-compete clause)--forbid that person from working at the new place during the term of the broken contract. The court cannot force the person to work at the original job, but it can forbid him/her from working in competition at the new place.
3. Since NIL contracts are essentially passive royalty payment contracts, not employment contracts (though they might require personal appearances, endorsements, etc.), they cannot be "pay for play" contracts (an NCAA rule). Thus, it is unlikely that an NIL contract would contain a "non-compete" clause like one might see in a typical employment contract.
4. An NIL contract would, however, normally contain an "exclusivity" clause. This is simply a monetary device. The purchaser of the NIL rights would have the exclusive commercial right to the player's NIL assets for the term of the contract, assuming the contractual payments were made paid timely and in full. This would mean that if booster no. 1 had purchased an exclusive commercial right to a player's NIL assets for a year, the player could not then re-sell his same NIL assets to a different booster. Because this has nothing to do with forced labor, a court would normally enforce that exclusivity right, by injunction and/or damages.
5. If booster no. 2 was aware of the existing NIL contract with booster no. 1, and nonetheless took steps to entice the player to dishonor the existing NIL contract and sign a new NIL contact with booster no. 2, then booster no. 1 would have grounds for a tort claim against booster no. 2 for "intentional interference with contractual relations" and/or "intentional interference with prospective business advantage." Tort claims normally are for monetary damages, which must be proven (might be tough for NIL contracts that are themselves fairly bogus in terms of commercial exploitation by the NIL rights buyer). A court might put on its "equity" hat and enjoin the booster no. 2 from entering into an NIL contract with the player, but there are some proof hurdles including a difficult showing of irreparable harm.
6. All of the above analysis is muddled further to the extent the player, in addition to an NIL contract with a booster, has signed a contract with the University to be compensated (presumably as an independent contractor, not employee) for playing football at the University. This would be a form of revenue sharing contract, permitted by the House lawsuit settlement, that most major universities (including the Gophers) are using to directly compensate players--i.e. "pay for play." If a player signs a "pay for play" revenue sharing contract with a University, the University could never force the player to play (13th Amendment) but could probably, during the term of that contract, enjoin the player from playing for another team that was a "competitor."
I could go on, but you get the point. This is complicated, muddled and disjointed area of law because the NIL contracts with boosters and the revenue sharing contracts with Universities have fundamentally different approaches that in some ways conflict. This is why pro sports have long ago move to complicated and comprehensive collective bargaining agreements: to lift matters out of the statutory and common law morass.
The Duke/Miami dispute is therefore, I believe, likely to be settled with an agreed payment from Miami to Duke and/or the Duke booster who holds the original NIL rights--simply because Miami has the money to get such a settlement done. If Miami didn't have the resources to fund such a settlement, the QB might return to Duke voluntarily, without court compulsion, because of the threat that he (1) he might be judicially enjoined form playing for Miami and (2) might not be able to collect NIL from Miami boosters. And he, or somebody on his behalf, would have to spend a lot of legal fees to find out.