They are instruments of the State. In Seattle, for example, the King County prosecutor’s office brings criminal cases as “The State of Washington v. John Doe.”
That seems to say he can do it, but only if he pays him. I don’t see anything about requiring him to consent, which is his issue. Nor about how much he must be paid.
Unless you have something else, that would seem to indicate that he would at least think he could do it, prohibiting any sort of lawsuit against him for trying. Plus, even if there is a consent requirement, how is he to know he didn’t consent before assigning it?
I do think it’s probably political theater. Does the governor have any challengers in the upcoming election who can use this against him?
He’s served his two terms and can’t run again. That won’t stop any candidate from either party to make fun of him, however.