Thank you!

Yes, multitrack editing would likely involve something DAW-like. Does the Korg software provide anything like that?

Does running in sync include that some units are on playback while others are recording (= overdubbing)?

I most often record several tracks of a tune in a live setting (all musicians in the same room playing together), and we build the final track by combining the best parts of these tracks. I could record everything in DSD, then mix the relevant parts on the analog desk, and then convert to PCM, and do the edits. Not ideal (reverb tails etc.), but possible.
Or choose the direct-to-disk approach entirely! I wouldn't mind working only with musicians who are capable of that.