There's a few issues:
As lotso people have said, and I got a printout in bold no less after extractions: DO NOT DISTURB THE BLOOD CLOT! So that is one practical concern about vaping after extractions. But that's only a concern in the first 24 hours or so. (Probably even less.) You do, after all, have to start eating and drinking again.
Then there is the nicotine issue and it ......ing the healing process. I'm not sure how clear this issue is regarding vaping and the dental industry. I don't know if the harm is from vaping in this case, or if they don't understand the significantly lower levels of nicotine we are exposed to compared to smoking. That, and if there is any "vaping is the same thing as smoking" conjecture going around that makes them believe the oral surgery is exposed to smoke and tar and all that other stuff when we vape, which, of course, it isn't.
Dry socket just happens. It happens to non vapers as well. I can see a possibility that the hygroscopic nature of vaping might contribute to that but - probably not. My extractions were sutured closed - it's not as if the area is directly open to exposure from vaping. I still got a dry socket on one of the lower jaw extractions. My Dentist said it's almost always the lower jaw extractions that have a dry socket problem and they don't even know why that is. Just went back the next day, she pooshed a piece of treated wadding in there and all was fine from that point on. And no - my dry socket wasn't a "child birth" event either. Just a dull ache that was there - when none of the other extraction sites had that. Didn't even know that it was a dry socket was until my Dentist said that's what it was.
Surely not medical advice: I started vaping about six hours after a six extraction extravaganza. Not a lot and I was doing really easy pulls. My Dentist said at follow up she was actually surprised at how quickly I healed - way ahead of the curve. Not about to say that was because of vaping either - I've always been a fast healer. Vaping in my case didn't cause any problems - that's all.