I do not recommend cats for rats.
1/ rats are awfully big for cats to handle
2/ cats will decimate your native birds far faster than your rat population
I can make an argument for cats controlling mice but again, they’re a bigger risk to native birds than mice. Plus outdoor cats get eaten by coyotes, foxes, raccoons, and loose dogs, not to mention hit by cars and attacked by other cats. No more outdoor cats for me.
If you want a ratter, look at what’s still being deployed for rats. Earth dog competitions are for ratters and you can contact breeders who compete in them and see what they’ve got litter wise. I will tell you that my now deceased Cairn was an excellent ratter and caught a couple in my yard despite having only about 100 sq feet of space to do the job in and a fence with holes big enough for the rats to slide through at any point. Used to catch rodents while leashed on our walks too. I’d have time to spot him leaping into the grass, here a snap, see him give a shake and the deed was done. Given a barn yard to patrol? He’d have been ecstatic.
My surviving Cairn was likely a puppy mill male and had to sort of learn to do normal dog things but I can tell you there are no rats currently in my yard, because if there were, he’d be heavily patrolling his little fence line rather than just a cursory sniff here and there.
To add: Cairns are not hypoallergenic but they are low shed and therefore low allergen. I don’t necessarily recommend sequestering any dog but they can be pretty independent. Better to sort out what you can handle hair wise and just do rat traps if you can’t have an indoor animal. At some point even a cat requires touching.