Neca lore (it is canonical) would indicate that the separation with the regular Predators and the Supers occurred at some point in Egypt. Why specifically the separation occurred we still don’t know beyond just a difference in tactics but one thing led to another resulting in a sort of blood feud.
Outside of the crucifixion of the classic Predator the Supers as a whole (though unknown what group) did attack a Predator colony. This incident would result in the “Ghost” Predator that specifically targeted Supers. Scavage would be a hybrid of the regular Predators and the Supers (he would resemble a Super though) meaning the two variants could breed and that not all Supers had been utterly bloodthirsty. As far as anyone can tell Scavage could get along with the others.
Ideas of the backstory for the trio from the film had been that they’d been exiled from the homeworld but nothing about that ever came up in the lore, it’d just been someone on production came up with. Berserker, Falconer, and Tracker however had been a clan of three at the very least with Berserker being something of a prodigy as far as anything went officially. Similar to the Jungle Hunter they weirdly never did all that much with the Supers whereas we have a ton of information of the AVP Predators.