The Wasteland Series is probably the most mainstream counterfactual in the world. It basically imagines if that brief period of post-war tension mixed with triumph over the entente just never ended, leading to a world that has become very different. Of course, the games are set long after the superbomb apocalypse, with the world before being a distant memory, but the pre-war world is fascinating itself.
In the US, we don't get much lore on it, but it's divided into multiple commonwealths in an attempt to break down national ties in the conquered Utah, Confederacy, and Canada while also engaging in general reorganization to make North America as a whole into a united state. These commonwealths serve to increase the authoritarian nature of the US, allowing the federal government to supersede state authority. This system also leads to corruption as some commonwealths are definitely far better regarded than others, while the commonwealths in the ex Confederate, Canadian, and Mormon nations are almost always governed by outsiders whom impose harsher rules. As a result, the United States of the Wasteland world is far more draconian AND far more unstable than in our world.
In the rest of the world, we don't get much beyond vague hints. Brazil is mentioned to be under integralists and the Tsar's Russia undergoes rises and falls. In Europe, the old American ally of Germany federates into Mitteleuropa, but also finds the United States distancing itself from it due to it's foreign policy being based around extreme anti-colonialism, as well as the Germans re-adopting Bismarckian policy on a global stage. At the same time, the US finds itself growing closer to Russia, leading to it becoming stronger, mainly as the US continues to fear Japanese expansion. While it's never made clear if Japan moderated or even saw the progressive faction take power as in our timeline, what is clear is that the Japanese are the main boogeyman to US plans in the pacific.
Eventually, the resource wars would begin. It should be mentioned that as culture stopped in this world, so did tech. Well, tech did advance, it's just that it advanced in a completely different way. This tech looks like the best stuff from 1950s magazines, but it also consumes a lot of Oil. This turns out bad when the world starts to run out. One of the major background wars that is mentioned is the Russo-Turkish war. From what can be inferred, the Russians got hit hard by the crisis (in spite of being a fuel exporter IRL, good on that one developers) and ended up opting to invade their old Ottoman enemies to secure their oil fields. What is known about the war is that the Ottomans apparently opted to detonate their own oil fields to prevent the Russians from getting their hands on it (it's never elaborated on what was meant by "detonated" but this map assumes the worst). Another thing mentioned is Operation Watersnake, in which the Russians apparently poisoned the entire nile river and killed most of Egypt in the process.
From this war, we also know that Germany got involved over their Ottoman allies being invaded. We don't know how the war actually turned out, but it's also mentioned that Britain and France took the time to attack Germany again when they were distracted, while it was also implied that the Russians had a lot of nukes compared to Germany, so this map goes with the idea that the Germans lost (although Petrograd and Moscow are explicitly mentioned in the cities that got superbombed). Either way, these wars are what inspire "Project Haven," leading to the creation of the infamous "Safehouses" in the US.
We also know that the US got into wars of it's own, invading Gran Colombia and Mexico. The US becomes a paranoid authoritarian state. Many starve, and things are worse in the commonwealths that aren't deemed "fully American." Funds are diverted to the army, and the security forces often go full mask off in the South or Canada, just straight up massacring rioters and protesters. Suspected rebel activity is clamped down upon heavily, and the Commission for the Preservation of the Union (abolished in 1975) becomes an effective secret police and propaganda force.
In the far East, Japan goes on it's own wars of expansion, having been hit hardest by the resource crunch due to being an island nation. The Japanese launch several invasions of their neighbors, leading to strong paranoia on the American end. The Japanese, seeing large amounts of dissidents across their empire and even on the homefront, end up invading Russian Alaska and the Far East, as well as invading Australia, bringing it into a two front war. To make matters worse, the Japanese launch a major strike against the American pacific fleet in the Sandwich Isles to ensure they wouldn't be a threat (the fleet had been stationed there just in case Japan did anything). We don't know much about the Japanese tech in the games, although we do see some Japanese guns, and the Assaultron robots we encounter in the fourth game are explicitly stated to have been copied from Japanese designs that saw combat in Australia. The Japanese are also mentioned to have a more advanced Navy, but a primitive army at one point. We also know that the Japanese used a lot of deadly chemicals in their wars, but that in the end, American Power Armor would seal the doom of the Empire.
There's also the inferences. India probably fell apart into Civil War rather than dissolve peacefully like IOTL, and the Germans retreating to their colonies is all inferred from me. What we do know is that the Japanese home islands eventually get invaded and this ends up leading to the Great War that leads to the titular Wasteland being formed. At the end, everything was erased to start anew. Gone is the United States of America, and in it's place are Iron Legion, the New California Empire, and it's rival in the Grand Armee.