Jeanette Nuñez is the Lt. Governor, and would replace him as Governor at some point if he wins the primary. She’s been in the job since 2019 and from all appearances would make a great Governor.
Campaigning is part of the process for all candidates, whether in office or not. Who was running the country while Trump was on the road in 2020? Fauci, from what we can tell.
He won’t win the primary.