None of these analogs are precise and, in many cases, the TL-191 nations are often mixes of OTL nations' roles. But here goes:
-United States: mix of France (a republic which came into the 20th Century humiliated in a previous war and guided by revanchism), the USSR (the rival power that was the direct enemy of TTL's white supremacist genocidal power; suffers major losses and a climactic Stalingrad-like battle at Pittsburgh; ends the war as one of the three world superpowers, along with being the most leftist power and the "standard bearer" for people's idea of Marxism) and Britain (an English-speaking world power with domestic politics divided three ways between moderate and reformist leftism, conservative capitalism, and a weak third party which is something in between).
-Confederate States: mix of Germany (a power that comes into the 20th Century swelled with pride from a decisive victory over its neighbor, only to be humbled and humiliated in the FGW, and then stain itself by starting the SGW, becoming a right-wing white supremacist dictatorship, and committing the century's defining genocide) and Russia (a conservative and backwards power on the fringes of European civilization; despite demonstrating industrial growth, is still largely agrarian; despite being considered a key ally of the Western European powers, is looked down on by them as reactionary and having a distasteful social system; experiences a communist revolution in the midst of the FGW).
-Texas: Poland (a part of a neighboring power a la Germany/Russia, despite having a distinct cultural identity and an undercurrent of wanting independence; the site of TTL's most infamous concentration camp formed when it was controlled by the right-wing genocidal dictatorship it was then a part of; achieves its independence after the SGW, but becomes a satellite of its superpower neighbor).
-Mexico: Romania/Hungary/Bulgaria (a minor power and satellite of its stronger neighbor which is swept up into joining their side even after said neighbor becomes a warmongering dictatorship; is complicit in TTL's Holocaust).
-Germany: mix of the USA (one of the three world superpowers; the fast-rising new, young industrial and military power of the 20th Century which stands as a colossus after the war and will likely be the biggest influence on western culture; "undefeated," so to speak, in the two great wars, which may foster a groundswelling of patriotism; was the first to develop and use the atomic bomb, which is both a testament to its scientific prowess and something that'll haunt them for decades as they are faced with the accusation that the atomic bombings constituted war crimes) and the Soviet Union (despite holding sway over Europe, was badly hurt during the war and will need a lot of time to recover)
-Britain: Japan (imperial island nation that was the last of the defeated SGW powers to surrender, was a major naval power, and had one last stand before going down in a blaze of multiple atomic bombings; transitioned from parliamentary democracy to militaristic right-wing nationalist quasi-dictatorship in the years between the two Great Wars)
-France: Italy (the originator of this world's most...erm, "orthodox" form of right-wing authoritarianism, with Action Francaise being equivalent to Italian Mussolini-style fascism in its early influence and its role as harbinger of something even worse)
-Austria-Hungary: France (a 19th Century power that has seen itself decline, relatively, from its previous position of power, but by virtue of being on the winning side of the two Great Wars, can still be a fairly influential regional power, even though its dependent on its allies to do so)
-Russia: China (a geographically large nation and potential major power, but spends most of the 20th Century as a chaotic basket case plagued by civil war, invasion, defeat and humiliation by foreign powers, and political radicalism. Hurting badly at the end of the war and is a mess, but once they somehow manage to get their shit together, the world better watch out).
-Japan: mix of USA (one of the three world superpowers which emerged from the SGW the least domestically damaged from the war, with all of its internal economic strength and infrastructure intact; a geographically isolated, yet extremely patriotic, militaristic, and potentially overconfident military power which has not yet tasted defeat in war) and China (despite being a superpower, is a geopolitically isolated, internationally distrusted pariah nation which has burned a lot of bridges with the rest of the world; authoritarian and harsh, at least toward its imperial subjects; the target of nationalist resistance from smaller Asian nations)