My 2 cents

Be professional. You didn't do anything wrong, so don't be harsh on yourself. As you said, the colleague had already had a bad reputation of gossiping and disrupting teams before interacting with you. These employees are the worst in the eyes of management. She would be let go sooner or later. It is not primarily because of you.

Also, it seems that you care too much to please other people. Many Chinese are like these. They want to make everybody around happy, which is impossible. It is not healthy, either, since it would put too much pressure on you one day. Think about it.