@Nonilex isn’t the key question here what constitutes official duty? I understand some level of immunity in the sense that a President may, as part of their responsibilities, have to act in ways that would otherwise be criminal (commanding troops to war, ordering imprisonment). Prosecuting for acts that are part of their duties would seem unfair.
I could see it argued that comms and actions related to an election campaign are not duties of a President, but as a candidate.