Does expiation become obligatory for someone who, in a state of anger, committed herself by a vow not to feed cats, and now regrets it and wishes to feed them?

If the aforementioned vow was merely a vow to oneself, and God's name was not mentioned in it, then it is not considered an oath, and nothing results from it. There is no harm in feeding cats or not feeding them, and God will not punish you for not feeding them unless you confine them or prevent them from seeking food. However, if the vow was made to God (such as saying: "Upon me is the covenant of Allah..."), then it is considered an oath by most scholars, and its expiation is the expiation for an oath. It is permissible to break it and offer expiation for it. In this case, feeding cats is permissible along with offering expiation for the oath.