The way the wikipedia article describes Bloom's definition is less generous than what you have here
> For Bloom, "[e]mpathy is the act of coming to experience the world as you think someone else does"[1]: 16
So for bloom it is not necessarily even accurately mirroring another's emotions, but only what you think there emotions are.
> Bloom also explores the neurological differences between feeling and understanding, which are central to demonstrating the limitations of empathy.
This seems to artificial separate empathy and understanding in a way that does not align with common usage and I would argue also makes for a less useful definition in that I would then need new words to describe what I currently use 'empathy' for.