Multiplayer/co-op

Greetings all ,my ps5 comes back from repair in a few days ,ive anno deluxe edition bought and ready to download as soon as I get it back and check over things on it

However my roommate would also like to get it or is considering it so we can play together for sone chill building and stuff

My questions are simple I know you just go onto multiplayer -add rival ,hold rival to add AI but what then?? Are we rhen pitted agaisnt eachother tk war ? Is there an end goal or can we change it so there isn't one and we just build play? Or can we just play with eachother in the same match we both have our islands and we just build up and trade with eachother ?? Conquer diff islands that sorta thing ? So long as I have my copy of the game and they have their own ?? Any help to explain everything about the multiplayer /co-op be greatly appreciated as this is what's the deciding factor in my roommate buying it