Would your cat tackle and catch a rat? We have one in the garden now but my cat either isn’t interested or is too scared of it. Previous cat was similar he had a white Ikea rattus rat toy which he liked to play with but one day he was scared of it, maybe he’d come across an actual rat somewhere.
My childhood tabby cat not very big used to catch a rat or more a day, dead and alive as we lived round the corner from a council dump and also there were issues with rubbish bins and an alleyway behind the houses/gardens. A rat only bit him once, he had to go to the vet.