It doesn't have to break up at all as the state already has long-standing legitimacy already thanks to the Habsburg dynasty which was affirmed (unlike Tito's Yugoslavia which revolved around him) by the victory in the Great War, and the suppression of the Hungarian uprising. Plus Kaiser Karl's death in this tl's has essentially made him into a sort of martyr for Danubia. And with the coming future industrialization, the Empire is bound to experience further prosperity giving its people even more incentives to keep the Empire together especially as it passed its trial by fire in the Great War.so Austria-Hungary could break up peacefully ummm don't know what to make of this
Things like Czechoslovak nationalism was a pretty fringe thing in otl and only really got off the ground thanks to the French seeking to totally destroy Austria-Hungary and create its own new set of alliances (The Little Entente) in the region. The original plans in an entente victory were at best to award Transylvania to Romania, the evacuation of Bosnia, Russian annexing Galicia, and granting Italy its irredentist claims in Dalmatia and in Tyrol/Trieste.