Questions About the DLC and Coop

Hey so the season pass is on sale on PS store until midnight so gotta make a decision quick. Me and a friend own the base game on PS5 and PC separately, she already owns the DLC so could we coop online without me buying it and how would that effect trophies and collectibles as I would like to get all the trophies and secrets but would rather save money if I can get it from playing with her. No spoilers plz