Proposal to Ban Ghost Jobs

This is explictly restricting speech (restricting the right to advertise for labor) and would have to meet a high first amendment bar in the US.

Pay transparency law supporters have argued successfully that there is a compelling interest in closing gender and racial wage gaps and that salary range information can be mandated in job listings for that purpose. What's the compelling interest in this case that allows the government to control speech?

How is this actually restricting speech? It's not restricting advertisements for labor, it's restricting intentional lies made to misdirect. That's called fraud.