I have not played Secret Hitler specifically, but in similar games (Mafia and Resistance) it is not in fact the case that members of the majority team should immediately share all information, and some of the best plays I’ve seen have involved members of the majority bluffing the minority.
(With that said, everyone following both of the first two bullets on your list above seems like clearly not a Nash equilibrium).
I have not played Secret Hitler specifically, but in similar games (Mafia and Resistance) it is not in fact the case that members of the majority team should immediately share all information, and some of the best plays I’ve seen have involved members of the majority bluffing the minority.
(With that said, everyone following both of the first two bullets on your list above seems like clearly not a Nash equilibrium).