you’re right of course, and for me the first panel the sentence sounds correct, but not the last one, where she’s already refering to her cat which is a cat like “gato” only. Maybe not the same asking if you have any car, any boyfriend or any cat as opposed to saying that now you have a cat, which should go with the “a” before. Unless the cat is called “Cat” 😅
I’m not a linguistic and cannot argue the why properly, but the sentence in last panel is definitely off