I read that to mean published scholarship or like a presentation at an academic conference or something. I can't imagine Columbia wants to know about my final paper from ENG 343, or my class presentation on Homi Bhabha.
That's true, though some schools ask/require LORs from work if you've been away for 2+ years. So while you should probably only use academic LORs for most schools, you'll need the work one for a few others.
I think you will probably have to send those transcripts, but I can't imagine that will look bad (I mean, make sure you get A's.). The fact that you have a conceptualization of academic pleasure is a good thing.
Is there a way to get the academic summary report without applying anywhere? I don't have LORs in the system and don't want to sign up for CAS yet, but I have absolutely no idea how to make the report run (if it's possible at all).