Is the failure to satiate a cat or the reduction of its food, while it enters and exits the home and relies on us for its nourishment, comparable to the act of the woman who entered Hellfire due to a cat?

A woman entered Hellfire because she imprisoned a cat and neither fed it nor let it eat from the vermin of the earth until it died. If you fear a cat's death due to lack of food, then take it out of the house and let it eat from the vermin of the earth. You are not religiously obligated to keep it confined and feed it.