I was trying to add this release by copying from this one, and the result seems to have only picked up the last disc (out of 4), though I only removed the vinyls from the new copy.
Is this a bug, or am I seeing/doing something wrong? Is there a way to fix this without starting over?
While I’m not sure how this ended up this way, you can definitely fix it - just go to the Tracklist tab, then Add medium, Existing medium and select the missing existing CDs (need to click Add medium once per disc though). Make sure they’re in the right order before submitting! 
Did you use the “Add release” button on the release group page? I think in that case mediums will not be picked if you did not visualize the tracks on the tracklist page (i.e. if you didn’t unfold by hand all mediums you want to keep)
I think there’s a ticket opened somewhere for this…
This may be what happened–I only expanded the chevron on the 4th disc, and that’s the one I see. (I added it using add release off a disc ID lookup.)