I know that this is supposed to be super thought out but like...
there are so many things you can do with pets some could be to boost your battle stats, and they could be used for battle
they could be an early and late game thing, they could give bonuses to crime, you could add an entire edu course for pet's pet armor you could add ways to get more pets, and you can just randomly get pets because randomly getting stuff is awesome, you could have really expensive hard to obtain pets through hunting but they would be like npcs and 1 person in an attack group could get it and yk you could have from pet rats to idk like bloop (The sea monster) or dragons but those pets would obviously be really late game, sorry I haven't thought this through I'm just thinking about how many things you can do with this.