Fallout pretty much died after Fallout 2. The new franchise has very little to do with the original game(s).

It's important to understand what Fallout went through before Bethesda even got their hands on it:

By the time there were plans for a Fallout 3, Western CRPGs had become a niche as the "RPG" label had become widely associated with "Action RPGs" like Diablo and RPG mechanics (skill progression systems really) had started popping up in many genres.

So rather than funding another RPG, Interplay decided to test the waters in a more promising genre: tactical action games. Because they lacked any experience with the genre, they outsourced the production of Fallout Tactics to a company unfamiliar with the franchise with very little input. The game was aesthetically and thematically very alien to the established canon. Some fans encouraged others to buy the game to demonstrate an interest in the franchise while others saw it as evidence that the series was dead. In the end it was a mixed bag but had very little to do with Fallout other than some flavor text.

With FoT not being nearly as successful as they must have hoped, Interplay made another last ditch attempt: Fallout Brotherhood of Steel, an action adventure based on the engine of an AD&D game that only had a moderate level of success. Instead of sticking with any of the core themes, the game heavily relied on language and dialogs written in a desperate attempt to appeal to teenage boys with an over-reliance on sexual themes. The press kits included glow-in-the-dark condoms. The game bombed, as expected.

Eventually Interplay did leak information about an in-progress sequel developed in-house with the code name "Van Buren" but Interplay had long been struggling financially and the game was eventually scrapped, though many elements would later re-appear in New Vegas (developed not by Bethesda but a company employing several people who worked on this and earlier Fallout games).

Interplay initially sold the licenses for Fallout 3, 4 and 5 to Bethesda. Still trying to produce their own take on the franchise they now spent their last resources on a Fallout MMORPG, temporarily titled "Fallout Online". "Fallout Online" (or "FOOL" as it had been titled by the community) had been an idea in the fan community for a long time but always been dismissed because the idea of an MMO game ran counter to the thematic constant of Fallout 1 and 2: the lone wanderer in a hostile wasteland.

If I recall correctly, part of the deal with Bethesda was that they would get the full rights to the franchise if Interplay did not produce another Fallout game within a given timeframe. The failure of Fallout Online sealed that deal. Ironically Bethesda's latest Fallout game is basically Fallout Online but based on their renewed franchise rather than the originals, but still an utter failure though for slightly different reasons.

Fallout's fan community, small but strangely persistent, at the time had been adequately described by game journalists as "glittering gems of hatred". I think that is justified to some extent: many of us would have rather seen the franchise die after Fallout 2 than move on and change. Some even argued that Fallout 2 was already overloaded with pop culture references (which to some degree had already been part of Fallout 1's DNA) and strayed from Fallout 1's leitmotif. But with the release of Fallout 3 it had become quite clear that this leitmotif had been completely abandoned.

For those unaware: While Fallout had always juxtaposed the optimistic 1950s Americana aesthetic and futurist outlook of technology and the "Atom Age" with the post-nuclear hellscape, the message was clearly a cynical dismissal of that optimism: nuclear power hadn't created a utopia, it created hell on Earth; instead of picket fences you had dirt farmers and scrap merchants trying to survive in an irradiated desert. Fallout 2 further emphasised this bleak outlook by showing that even the vaults that were supposed to protect American citizens from the aftermath of WW3 were actually cynical experiments, each being flawed in their own cruel ways, while the government elites get to live in safety (intentionally taking a page or two from Doctor Strangelove).

Fallout 3 eliminated any of the remaining bleakness and subtlety and replaced it with mini-nuke launchers and more Americana. Where Fallout 1 and 2 were satire, Fallout 3 had already lost the intent of that satire and just ended up playing it straight. But these themes were already mostly absent in Fallout Tactics and completely abandoned in Fallout Brotherhood of Steel: Fallout already died before Bethesda added to the franchise.