A friend who knows more about cats than I do said only 25% of cats will go after rats. I guess the rest are scared.
A full sized NYC rat or field rat is in nearly even terms with an individual cat only large males will tangle with them. If you have a pack of cats they will team up on a big rat just like their lion cousins pretty impressive little creatures I’d never let one live in my house as I don’t abide by letting an animal defecate inside the whole litter box thing is gross. My dogs know outside is their head call area or they get the hose again.