So what happens whenever Danbooru makes a bulk tag update? Do we automatically have a script that interprets that, does Jedi wake up at the crack of dawn to check and then do it himself, etc.?

Depends, sometimes we don't do anything. Othertimes Jedi will take action, but now we've got someone who is writing a tool specifically to sync our tags. I hope to one day have time to make it part of core, but I've got other things to do right now. :<

I think I'm doing most of this. The exception being when many characters from a franchise are updated at once like Pokemon going with English names. AngryZapdos handles these.

I see what aliases and renames got approved at Danbooru.
Implications are automatic now so I don't have to mess with them any more.
We aren't aliasing artists the way Danbooru does so those and any tag renames are handled with the mass tag editor.
I put all the other approved aliases into our alias request page for Jerl to approve if he wants.