So what laws might apply?
The FTC says:
"The Sherman Act outlaws "every contract, combination, or conspiracy in restraint of trade," and any "monopolization, attempted monopolization, or conspiracy or combination to monopolize." Long ago, the Supreme Court decided that the Sherman Act does not prohibit every restraint of trade, only those that are unreasonable."
https://www.ftc.gov/tips-advice/competition-guidance/guide-a...
So maybe enormous power could be found in the executive branch by simply declaring that non-competes are "unreasonable" and defending that in court.