Why trifarian pit war does not trigger mighty but assault trigger mighty

Yes — the premise is right: Assault can make a unit become Mighty, but Trifarian War Camp doesn't, and the difference is whether the unit was already on the board when its Might changed.

"Becomes Mighty" only happens at the moment a unit's Might goes from under 5 to 5-or-more while it's on the board (Rule 709, Rule 710). War Camp's +1 is continuous and already factored in as the unit enters that battlefield, so a printed 4-Might unit is never a 4-Might object at War Camp — it appears at 5 and there's no transition to detect. If you instead move an existing 4-Might unit from your Base to War Camp, that does trigger "becomes Mighty" effects like Fiora, because the unit is already on the board when the +1 lands.

Assault is different: the unit is genuinely sitting at 4 Might on the board, then gains the Attacker designation during combat and the +1 applies at that point, so its Might really changes 4→5 and it becomes Mighty (FAQ #618). Two practical limits: Assault only applies while it holds the Attacker designation, so it can't make a unit Mighty on an empty battlefield (no combat, no attacker designation), and the Mighty status ends when that designation is removed.