so the vibe is meant to be retrofuturism or Raygun Gothic. Basically everything but the evil commies (became Chinese instead of Russia) stopped at the 1950s, the music, the clothes, the cars just stopped at the 50s look and feel more or less.
That's only a part of the Fallout vibe.
One of the big issues Bethesda had was that they saw that as 100% of the vibe. But it isn't. FO1/2/NV were intentionally a collision of multiple different vibes - the '50s retrofuture was just the one most unfamiliar to most people so tended to stick out. There's also a big Mad Max vibe, a more modernist vibe for the NCR, which is consciously post-50s in the way it is designed, and the Enclave originally had a big men-in-black/deep state (before that became an idiot's term) vibes, which were distinctly more futuristic still - you can see this incredibly easily in the design of the Enclave's power armour, for example. And there's a whole bunch of Western stuff going on too - which this show goes pretty hard with I note. There's also a general rugged industrial-ness going on that's actually quite post-50s, in 1/2/NV, with a lot of stuff that's more 60s through 80s - including quite modern weapon designs. FO3 completely skips all of that (understandable with the Western stuff as neither it nor FO4 are in the West, but the rest was dumped because they didn't get it - people were pointing this out as far back as the original reveal of FO3, note), and only does 1950s, even dragging stuff like the raiders and so on, who had Mad Max vibes, into become 1950s-style greaser gangs and the like, and completely abandoning all rebuilding, just having people all be stuck in time in ways that make no sense. It's particularly bad with the Enclave, because it loses their entire aesthetic concept despite them being a major element.
FO4 improved things slightly, but only by reinventing the wheel - The Institute has 1960s and 1970s design aesthetics to make them look relatively more futuristic, which ends up making it look slightly NCR-ish. It still has everyone else cosplaying the '50s in a way that makes zero sense - the people from the Vaults should absolutely be doing that, but cities which have been around for 200+ years? They'd have their own whole takes, which might well reference pre-war styles like post-Roman societies referenced Roman ones, but which wouldn't just be cosplaying in dirty, worn costumes. It's so ingrained that even the awful crappy early villain of FO4 is basically a 1950s guy in a way that just makes it seem like he stepped out of an attempt to make Full Throttle (the OTHER 1950s vibes post-apocalyptic retro-future! Actually predated Fallout) edgier.
The show used more of the aesthetics than FO3/4, including, notably, the NCR Ranger armour, presumably to show a certain character was a retired Ranger, and it looks notably higher-tech compared to a lot of what we saw, distinguishing it as being from a different aesthetic culture (the NCR as opposed to pre-war). Also I think that they had guns that looked like they'd escaped from various FO games, from FO1 to FO4. In fact I can confirm that thanks to
this! There are also appropriately janky-looking real-world weapons, which all Fallout games have done.