Problem is that with this, proving that it fell under one power basically means all other laws, even ones that specifically were meant to restrict that power, are meaningless. What he did could be 100% illegal, but he can’t be prosecuted for it, so he can’t be removed from office or punished after he leaves office.
If he was making that call as the official president of the United States, speaking in an official capacity, then it doesn’t matter if the order he gives is illegal if it was within his power to order the Governor of a state to do anything at all. If it’s not in his power for him to give an order to the Governor, then he just has to say it was an official suggestion as the president of the US. There’s no restriction that says a president can’t suggest that the Governor of a state does something to benefit the president. Doesn’t matter that the thing he asked for was illegal because it can’t be questioned in court at all to determine its legality.
Now it depends on if the Governor were to actually do it. And if as president Trump decides to order the assassination of that Governor once he refused, that would not be prosecutable. The assassin would be the only one who could be punished for the illegal act.
Immunity from prosecution doesn’t mean the thing you’re doing isn’t legal, it means that no one has the right to punish you for that act. It’s still unethical to break the law, but there is no enforceable consequence.