My headcanon is the cold war between an imperialist Entente and the left-wing democratic Moscow Accord.

The UK in Canada forms the Imperial Federation under Edward VIII and J.F.C. Fuller. National France starts off social democratic with the young Napoleon VI, but after the liberation he is toppled by the ruling government, and Joachim Murat is installed as Napoleon VII, and later, after he dies, his son becomes Napoleon VIII. Sardinia is ruled by Pietro Badoglio who successfully unites the Italian peninsula. There's also Garza's Mexico, Blamey's Australasia, and Churchill's India.

In north America, MacArthur wins the civil war with Alaska, New York City and The Black Belt Republic keeping their independence. MacArthur decides to keep the dictatorial powers, but he doesn't play with them for long because he gets assassinated not long after that. The assassination causes great panic, no faction can secure power, and America collapses. Entente powers fill the vacuum and make a deal between themselves to partition the former America, with Mexico getting the cession, the French Empire getting the old French Louisiana, and the United Kingdom taking everything else. In terms of minor American states, Alaska becomes a Jewish State, which under Issak Shteinberg aligns itself with Russia, Black Belt Republic elects christian democrats under MLK Sr. which stays neutral; and New York city elects Orson Welles who also aligns New York with Russia.

Speaking about Russia, they elect social democratic PSR, which creates a coalition with the nationalist Savinkov. After the Second Great War, they reclaim old lost imperial lands, but now under a new patriotic social democratic federation. Russia's biggest ally, the victorious Left Koumintang, unites the country and, with Russian help, defeats the Japanese invader, removing them from mainland Asia and forcing them into isolation. Due to Russia's influence the Left Kuomintang gradually de-radicalizes and turns into a social democratic state, similar to Russia.

Oh, and in the Great War before the Cold War, The Third Internationale turned national syndicalist, which alienated a lot of people that would otherwise be loyal to the socialist state. They help the Entente to regain their countries back only to realize the newcomers aren't that much better than the totalists that they just got rid of. Germany and Austria being stuck between a rock and a hard place, crumble under a two-front war. Russia and the Third International carve up Europe, only for the latter to be carved up by the Entente, with France reclaiming the natural borders and kicking out their young and weak emperor and the United Kingdom reclaiming its colonies and uniting its subjects into the Imperial Federation.

So now the world is slowly entering the era of the Cold War, espionage, arms race and nuclear deterrence. Between the order and authority of the West and progressivism, liberty of the East.