-Shady Sands and The Boneyard looks like they were re-nuked yesterday, there's no sign of NCR civilization (perhaps a canonized Lonesome Road ending)?
The shot with the sign that says "Shady Sands" very clearly has gigantic, 21st century metropolis-level ruins. It maybe even looks like LA specifically. So if we assume based on the sign the scene depicted is Shady Sands, either the location has been moved to LA, or they've retconned that Shady Sands was built in or near a pre-War metropolis, instead of the middle of nowhere.
Both of these are far too ridiculous for me to believe Bethesda would do. It would be by far their largest retcon/mistake, literally nothing would come close. Generally they get details wrong, or the spirit of the lore, such that some justification can usually be made. This would be so vastly and outright wrong that I can't believe they'd make this mistake, or even that they'd allow TV writers to make that mistake.
I think more likely is that the library sign we see is just some library organization, originally from Shady Sands, and this is a library of theirs in the Boneyard.
-BOS has a million Vertibirds and the Prydwen (which was canonically built out of the Enclave crawler from Fallout 3's Broken Steel DLC, so unless they happened to find another crawler on the West Coast, this might be THE BOS from Fallout 4 coming back to California)
It's not the Prydwen, it's some other airship according to promo material, though it also has an Arthurian/Welsh name. Annweden or something around there. Can't rule out the East Coast BoS has joined. My gut says no,, that they haven't come back explicitly, just that they shared designs or something equally stupid. But who knows.
Bethesda has deemed this show 100% canon to the games timelines, so either Chris Avellone was right and the classics aren't canon to Bethesda, or Bethesda hates the classics this is their way of giving them the middle finger?
C'mon, let's not be silly. They just don't care