Alright, let's take a crack at this. OP says "before or after the pandemic" but truth be told even after the pandemic COVID will still exist for some time. More likely we're looking at pre-pandemic, when the US is led by...oh.
So, yes, the USA has just lost its government and while DC circa 2019 probably has a full government, outside of DC proper and San Francisco[1], not a single American voted for any of those officials...so, while perhaps some emergency or transitional government could be negotiated, the hand at the wheel is not exactly the most stable, so who's to say how bad things could get? Or who the downtimers will be able to assemble to negotiate on their behalf?
Shit, maybe San Francisco wouldn't even want to rejoin the Union, given the culture clash[2] - DC residents are also majority Black and overwhelmingly vote Democrat so they would have some really strong objections to the state of affairs, but DC's cultural and political importance make city-state status a non-seller. That said...looks at sustained race riots in DC throughout the past year. Well, it would be interesting.
On the other hand, this is the Great Depression and the communist movement in America is very strong...one could see leftists from DC and SanFran moving among the masses, trying to organize and influence events, even uptime politicians who've lost their home states might schlep around trying to restart their careers.
London, as mentioned, may be the most immediately stable. There may be some issues, as with America, as to elected officials not actually being elected, and there might be problems with the Royal Succession if a member of the Royal Family was outside London at the time, but the UK could probably hold elections quicker than the US and Greater London has more than enough clout to get a favorable deal. Of course the problem will be culture clash, not only issues of race and gender but the fact that London comes from a post-Empire world...while some fools may try and keep the Empire or "reform" it in some way, I think most Londoners, especially those of African or Indian descent will have some...objections.
And they might lodge those objections in the voting booth, or in their time-shifted homelands. Those ventures probably won't be extraordinarily successful - they'll have as much culture clash as the Brits - but it will conplicate things.
Paris is similar to London; different ethnicities and cultures, different government. Maybe they'll have a revolution just for kicks. France probably also has problems with the Imperial question, I'm not sure who would have an easier time holding on to theirs.
Berlin is going to do everything to keep the Nazis out of power. They could probably take power in the unstable Weimar Republic, and honestly if there's one place I'm optimistic about it's Germany; then again, for historical and alternate-historical reasons they will be Concerned about Russia so I can see some form of intervention there, as neither the Soviets nor Putin seem like they'd make good neighbors.
Moscow has been discussed a bit, but I want to stress that governments are not the only actors here - and there are modern Russians who oppose Putin who even have nostalgia for the USSR - and this is a USSR that has yet to make certain historical mistakes, no less[3].
Beijing, Hong Kong, and Taiwan have been discussed at length; China was not a stable part of the world and is unlikely to remain that way.
As for Tokyo, we have the same problem as London where both the elected government and the monarchy are of dubious legitimacy, and while modern Japan has some...history, Tokyo has just accidentally'd into their own empire once again and whatever direction the new government takes, they will have to think very hard about Japan's place in the world. I should also say that modern Tokyo will have as many issues on gender, race, and so on as London, Paris, or Berlin.
It's probably worth address that tension - will modern social values be embraced or rejected? Will progress, as we see it, be greatly advanced, or will it be smothered? Will great mistakes of history be avoided, or will new and worse ones be made?
Ultimately I think it will be both, in various places[4]. Some places will move forward remarkably quickly, or the ISOT could provide the spark for a transformative wave of liberation across the world...while in other places modern technology just entrenches unjust regimes even further, or the shock of the ISOT wipes away whatever progress may be had.
Here are but a few possibilities:
- the British Empire dissolves, partly due to intense pressure from London and partly due to economic and political chaos making colonial campaigns difficult; decolonization is still messy, but a few uptimers are trying doggedly to bootstrap the former colonies. Some descend into bloody conflict, but India isn't partitioned as a different set of nationalists come to prominence. Other empires try and fill the vacuum, and the UK tries to find its way in the world.
- France experiences a revolution and the new liberal-nationalist govenrment attempts to reform the empire into a federation; Indochina is given up as a bad job, but Francophone Africa gets some investment. The result will be a regime that is both all-inclusive and all-oppressive, using the best of 21st Century social controls to assimilate Black Africans into French culture. Some African elites (and educated uptimers of African descent) will benefit, so long as they're properly Francified.
- Japan skipped liberalism and went straight to neoliberalism. They're imperialistic (although it's an empire of economic and political puppets), they tried to get involved in China and ate shit, but they did get to be top dog in the Pacific. Socially actually kind of nice, and the GEACPS has more staying power since it's built on "alliances". Some people are getting very rich. It probably still won't last. Has nukes.
- Germany ultimately shoots ahead on social norms, actually improving on us in some ways, European Jewry flourishes (outside France). On the flip side, Germany and the USSR fight over Eastern Europe and that snowballs into WW2. Some things never change.
- Right, the USSR. A coalition of anti-Putin uptimers and downtime Soviets managed to put the country together. The USSR managed to avoid some Mistakes (and made some others). They're a lot saner economically, sort of okay socially, but they're very aggressive and nationalistic. Not as oppressively paranoid as OTL, still very optimistic and into scientific progress. Think the ISOT was done by communist aliens.
- China's civil war got a lot messier after the ISOT, and although Taiwan made a real go of it with Japanese assistance (which may not have completely helped their case), the PRC wound up uniting the place. Currently they are struggling hard to bootstrap the country up to the point where they can make themselves a serious player. Hong Kong got really ugly but some other countries have made good use of the Hong Konger Diaspora. Trying to buddy up with the USSR, though the USSR is put off by their I Can't Believe It's Not Communism![5] and the nationalist side sees them as a threat. Has nukes and wishes they'd wasted Japan before they got nukes.
- Taiwan is a member of the GEACPS, but in a very "France and Germany in the EU" relationship - definitely an actual player. After losing the Chinese Civil War a new government came to power that officially declared itself the Republic of Taiwan and surrendered any claims to the mainland. That probably won't help them any.
- The USA had problems. There was no coordinated repsonse among the downtimers with coalitions of state governors butting heads, the military stepping in, the uptime government having no idea who they were even supposed to get the support of, and 45 not...helping... Add in the residents of DC proving to be extremely stubborn and hey presto, it's Civil War 2. Uptime leftists managed to forge a coalition of urban unions (promising worker control of industry), African-Americans (promising an end to Jim Crow), and bankrupt farmers (promising an end to debt), and only recently swept up the pieces of the old regime. Things look, and feel, pretty bright for the Union of American Soviets, and while some things got messed up, they have kept their promises. That said, Japan managed to snatch the Philippines and Hawaii away as puppets, Canada is looking nasty, and there are bigger stormclouds on the horizon...
Other stuff:
- the Spanish Civil War broke out a few years early and was won for the commies
- someone (probably the Germans) ganked Mussolini and a new government styling itself off of France is getting owned by an Ethiopia that someone (probably the Americans) gave uptime weapons
- Canada and Australia are really pissed at Britain for leaving them, really scared of the UAS/Japan, respectively, and turning pretty fascist as a result
- South Africa has an ongoing civil war
- India is doing well, they're trying to copy Nasser
- the Middle East is a mess, with Egypt trying to unite North Africa and kick out the French, a Hashemite-backed Pan-Arab movement, and a Persia that went communist; the Republic of Palestine is shaky - three governments have come and gone, but the current one is secular, and while the Kibbitzim are actually doing fairly well, the Zionist movement has been a bit chilled for now
- things actually happened in Latin America; Brazil and Argentina went fascist, invaded Chile, and are looking at the rest of the continent greedily; the Banana Republics were toppled and Mexico and Peru are increasingly friendly with the Comintern; if Peru jumps ship as well, there will be blood
- vaccination programs are making good headway, the League of Nations was dissolved with no replacement (except maybe the Comintern), and the Great Depression has ended
- uptime technology and information has been widely disseminated; only Europe and Japan have teched up enough to reproduce even a 1970s level of technology, although the UAS, USSR, and PRC are working hard to catch up. More than that, uptime ideas have flourished, from women's liberation and uptime insurgency techniques to governments picking up propaganda, social controls, and counterinsurgency techniques, and of course a mania for uptime pop culture.
...
- China and France hate Japan. The Cominterm - the UAS, USSR and allies - keeps gaining members. Germany and Russia hate each other. The Japanese and French want to keep expanding their empires. The fascists, though strangled in the crib in Europe, have taken half of South America, and are on the verge of victory in Canada and Australia. Africa is a patchwork of colonies, communists, nationalists, warlords, and others. China and Japan have nukes, and who knows what other countries aren't far behind?
There will be a World War 2. And something will be born from the ashes. A new world. A better one? Perhaps. Perhaps not.
There are many possibilities.
[1] Ironically I think Nancy Pelosi is the sole member of the Federal Government who actually has voters...go figure...
[2] Not that the I believe the past is inherently more bigoted - Weimar Germany had a thriving LGBT scene and some pioneering work on transgender people was being done, before the Nazis, and IIRC the Soviets had yet to criminalize homosexuality either. Many downtimers will be amenable to modern social norms! But well, this is pre-Jim Crow, after all...
[3] Although some mistakes may be unavoidable at this point...and much of the nostalgia for the USSR in modern Russia has less to do with communism and more with nationalist admiration for a Russia that stood tall on the world stage...
[4] Okay, ultimately this is pure imagination and as a writer I can decide this goes any way I want. If I want this scenario to produce Fully Automated Luxury Gay Space Communism, I can find a way to justify it, and if I want soul-crushing grimdark or the early triumph of multicutural liberal democracy, I could do that, too.
[5] Mao was ganked, the communists rallied to Beijing's red banner, and between that, Xi Jinping Thought, and some True Believers, things got ideologically spicy.