it’s a more general word.
including “a feeling of loyalty” and “unity or harmony in action or effect.”

Sure, you could be a “sympathizer”, but those meanings I feel are out of scope of what Kirk was talking about.

empathy is about a serious effort to imagine or understand another’s experience as if it were one’s own, which sympathy doesn’t imply.

I don’t think empathy implies any serious effort. Empathy is something you just have, or something you experience/feel, rather than make an effort to “do”. It’s innate (in some).

I’m not sure I understand your last question.