I don't quite understand whether the Gold Edition is a new build/rerelease, or just a new, more complete pack.

I'm not quite sure I understand what your doubt is about. The differences between those is that Gold includes the two paid DLCs (and 20 new player character portraits apparently), which Deluxe does not.

Deluxe is just the "with extras" edition that came out on the original release date, and Gold is the "definitive" edition that came out after the devs were done with the game.