2 of 2 no questions in the answer, following a comment.

Let us describe a very simple system that does something we could label as empathyc.

A chatbot answers "I am sorry to hear that. What happened?" when we type "I feel bad", and it replies "I am glad to hear that. Fancy some music?" when we type "I feel good".

Somehow, it perceives a human emotion, and acts accordingly.

Planes fly but they do not fly as birds. Similarly, we can expect artificial empathy from an AI, not necessarily natural empathy as we feel it.