The USA will pursue a postwar policy of reunion with the former CSA. The USA will also gradually bring the military occupation of former Canada to a close, in favor of granting statehood to the former Canadian provinces and pursuing a policy of political reconciliation north of the former border.
Texas may remain independent for some time, but I think that Turtledove has said that Texas would eventually be brought back into the Union. In the continuation of TL-191 that I wrote, Texas remains independent because of a large influx of immigrants from the former CSA, some three million people in all, who refuse to live under US rule.
The USA will do what it can to help the African-American survivors of the genocide carried out by the Featherston regime and the Freedom Party. I suspect that the vast majority of survivors will want to leave the former CSA.
The USA will also spend the first generation after the end of the Second Great War consolidating control over North America. I could see the Dewey administration moving to take Alaska from the Russian Empire, in order to avoid the possibility of Alaska being taken by the Japanese Empire.
In the continuation that I wrote of TL-191, I imagined that the USA forming a military alliance with the other nations of North America, along with certain other countries overseas. This would lead to the USA investing in the military and transportation infrastructure of its allies, in order to facilitate a rapid US military presence during a future crisis. I also imagined that the USA would gain full control over the former British and French colonies in the Caribbean.
I do not think that the post-SGW will have an equivalent of the USA-USSR Cold War from OTL. The international situation will be similar to earlier eras of great power competition. Of course, this would be complicated further by the proliferation of superbombs and the development of deadlier weapons.
Unless I’m mistaken, I think that it’s hinted at the very end of the series that the USA intends to work with the German Empire in an effort to halt the proliferation of superbombs. I could imagine the USA, the Austro-Hungarian Empire, and the German Empire cooperating during the first generation after the end of the SGW to prevent other nations from acquiring superbombs, although Austro-Hungarian and German efforts would primarily be directed against the Russian Empire, while US efforts would primarily be directed against the Japanese Empire. I don’t know how successful these postwar anti-proliferation efforts by the Austro-Hungarian Empire, German Empire, and USA would be.
The post-SGW world of TL-191 would be very different from the post-WWII world in our world. I think that it would be more economically austere and militarized than IOTL. The effects of multiple cities being destroyed by superbombs around the world at the end of the SGW will also be severe, and will be reflected in the postwar economy and postwar culture.
Ultimately, the USA in TTL would have little resemblance to the USA in our world, in terms of its domestic politics, military policies, or wider culture.
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This is what I previously argued about why the USA would pursue a postwar policy of reunion with the former CSA, slightly edited:
I would argue that from the perspective of the US political and military leaders in 1944, and likely during the first generation after the end of the SGW, there are several overarching factors that would favor a policy of reunion, versus allowing for any region of the former CSA, barring Texas, independence.
-The USA under Al Smith was beyond accommodating to the Featherston regime, to the point of ceding Houston and Kentucky back to the CSA. As another AH.com user remarked in another thread, this is equivalent to France in OTL 1938 ceding Alsace-Lorraine to the Third Reich. The end result of this policy of appeasement, of course, was Featherston launching Operation Blackbeard and the CSA managing to split the US in half. The lesson likely learned by US policymakers after the war is that any territorial concessions to an enemy of the US will invite an attack. The USA will not allow for the possibility of a hostile foreign power on its southern border again.
-The Destruction. The crimes of Featherston and the Freedom Party add a moral dimension to ending the independence of the CSA. The US will also not tolerate the possibility of such a monstrous regime existing on its southern border again.
-The USA arguably since the War of Secession, and definitely since 1881-1882, has faced the specter of encirclement in North America by hostile foreign powers. While this was lessened after the FGW with the defeat and occupation of Canada, this sense of an existential threat to the territorial integrity and the independence of the USA was likely brought back into a forefront of US popular conscience by Operation Blackbeard, the Second Canadian Uprising, and yet another Mormon revolt. With the final defeat of the Canadian and Mormon rebels and the fall of the CSA, the USA, for the first time in many decades, is free of the possibility of encirclement by hostile powers. The USA will not tolerate the presence on its southern border of a potentially hostile foreign power that could ally itself with an overseas enemy of the USA.
-Since the War of Secession, the USA in TTL has lived with the shame of military defeat and the failure to preserve the Union. With the defeat of the CSA, that national shame has been brought to and end, and the USA can finally reunite, as should have occurred in the 1860s. I do not think that the USA will willingly abandon the project of reunion after the end of the SGW, especially after four North American Wars, each worse than the last.
For these reasons, and likely others, I think that the USA will proceed with a postwar policy of reunion. These are also the reasons why I think that the USA in TL-191 is highly unlikely to allow for the establishment of multiple independent states on the territory of the former CSA in lieu of annexation and reunion. I cannot imagine the post-SGW USA willingly going back to a prewar situation of facing encirclement in North America from enemies.