Is the questioner sinful and is expiation (kaffarah) binding upon her for the death of her cat, given her feeling of shortcoming and negligence in its treatment?

You are not sinful for the death of the aforementioned cat because sin is incurred by whoever intentionally confines an animal with the purpose of harming it, neither feeding nor watering it until it dies, as mentioned in the Hadith. It would have been more appropriate and beneficial for you to spend the money on needy Muslims. We advise you to stop dwelling on this incident and not to be overly scrupulous about it.