> Modeling someone’s cognition or experience is not empathy.

then what is it? I'd argue that is a common definition of empathy, it's how I would define empathy. I'd argue what you're talking about is a narrow aspect of empathy I'd call "emotional mirroring".

Emotional mirroring is more like instinctual training-wheels. It's automatic, provided by biology, and it promotes some simple pro-social behaviors that improve unit cohesion. It provides intuition for developing actual empathy, but if left undeveloped is not useful for very much beyond immediate relationships.