when 2 fed-alligned factions are at war feds fight on both sides.
This one
Superpower doesn't determine whether two sides go to war, factional ethos does.
Not listed in game, but all factions have an underlying ethos, one of Authoritarian, Social, Corporate, Criminal.
With the exception of Criminal ethos (who go to war with everyone, even other criminals), if two factions are of the same ethos, they go to Election, otherwise they go to war.
So for example, Dictatorship and Patronage go to Election, as they're both Authoritarian, but Dictatorship and Democracy will go to war (Authoritarian vs Social)