you have a few "objectives" to unlock some perks / emotes / dance. Will also unlock some additionnal parts of the game (like killing the kraken lets you build the submarine, which lets you explore the great depth, tame karkinos, etc....
But there aren't any story mod or quest. But that would be a great thing to add to the game, having NPC's on some of those 200+ islands. Would give more meaning to the exploration, and looooot more content to the game.