Barn owls eat mostly smaller mammals. The list includes rats and mice, but could also include starlings, blackbirds, and rabbits, if they’re small enough. Squirrels and other rodents this size and above are typically safe from barn owls as they can’t eat them, and they’re diurnal instead of nocturnal. Since barn owls are nocturnal, their prey has to be nocturnal as well. This means that many animals humans are used to seeing while out and about during the day - squirrels, dogs, etc. - are safe because of size, activity time, etc.
However, barn owl populations are declining in some parts of the world. This isn’t for a lack of food; with more humans in every part of the world, rats and mice are thriving like never before until they’re caught by the humans. It’s due to habitat loss.