hi!!!! I'm the number one Corrupted Puppeteer fan in the entire universe so I can actually give some context.
First off, we have no fucking clue what the Anomaly is. Only that it received Lodi's message from Kepler. It will forever remain unexplained and exist only to take cool photos of the suppressor man with.
The Puppeteer itself is Clovis' attempt at creating an artificial Vex mind. This is explained by Astraea in the logs from the questline pretty much nobody did because it had math or whatever. Of course, like everything Clovis does, this went terribly wrong. The Vesper Station got abandoned for reasons that might have been explained but they escape me right now, and sat there for years.
Then you and Taniks crashed the Morning Star during the events of DSC.
Debris from the wreck hit and ruined the Station, and let the Puppeteer escape. You can see where it was originally contained in the first room you enter!
The Atraks specifics are unclear of whether it's the core Atraks' corpse or an extra frame. Given that Atraks is smart as fuck and we see a ketch during the spacewalk, it's likely she was controlling the clones from outside of the Crypt. It was hinted at back during Pantheon that we didn't kill the real Atraks anyway, and that if she is dead, there's a back-up of her somewhere on Europa. Alas, plot threads that will never be explored.
The Puppeteer was also the second boss when you fought it, because of it being able to jump bodies. Astraea will tell you this during the 1-2 transition if you've done the full questline + the binary puzzle needed for the title and instant Ice Breaker masterwork.
Likely due to some combination of Exos being BrayTech stuff and Vex being mechanical goblins, the Puppeteer was able to inhabit the copy. When Salvation defectors arrived and tried to make their home on the Station, it basically stalked each one of them down and did something to integrate it into it's own kind of hive mind. Like a miniature Vex network, I'd reckon? Given what the Puppeteer is and everything. That's why, as Spider points out in the quest, all the creepy SIVA looking wiring around the station is a mess. The Puppeteer is controlling every single body in the station. And the Puppeteer is really bad at wirework apparently.
Notable fun facts include:
-You can see skiffs moving back and forth hauling materials to the anomaly in the skybox. Unless they're building the Anomaly entirely out of the Vesper Station remains, this implies that the Puppeteer's mental network has a ridiculously far extension
-Atraks clones in DSC dissipate upon being destroyed, but puppet corpses stay after death. I've thought about how this could work, that perhaps the puppets we fight are being converted from regular eliksni, but it seems to produce the puppets in the exact same way Atraks produces copies. Regardless of what the reason behind the corpses remaining is, at least you can get some really funny clips out of it with Destiny 2 corpse physics.
-It has a different gun from Atraks (a Wire Rifle over a Shock Rifle. Or QB over LoW)
Anyway I will vanish off into the night now. I just needed to Puppeteer post. I have been thinking endlessly about both Atraks-1 and the Corrupted Puppeteer since Vesper's Host first came out and given how much the dungeon means to me, I will probably be thinking about them forever.
Friendly reminder to anyone tackling the dungeon - it's one of the hardest pieces of content in the game, arguably harder than some raids, but it's worth it for the atmosphere and story. Also the cool looking armor. That's the number 1 priority.