I've pondered this question many times for my own timeline, and many of the answers are complex and messy.
In my own timeline, the answer is still a failure of the A-H, but its successor states are eventually able to move beyond the spectre of authoritarianism and they have a calmer and more level-headed second half of the 20th century as a result. There is far less damage to minority communities (including Jewish ones) during the nastiest parts of the 20th century, but even with that lesser destruction, people thankfully take lessons from it and know what to avoid. In a sad irony of history, I quickly realised just how oddly "alien" everyday life would be in a post-A-H central Europe, where Christian churches and Jewish communities continued to coexist en masse on a daily basis, due to no holocaust or similar persecution. Already years ago, I explored this topic in
this particular thread. Whenever I write some little narrative or idea in that timeline's setting, I keep reminding myself that Jewish citizens (in either an ethnic or religious sense) wouldn't be a rarity, they'd be a frequent site, alongside all the other nationalities.
One cultural event that also occurs in around the 1960s/1970s in central Europe, and has shades of the OTL Maori Renaissance of New Zealand, is a Romani Renaissance. Given OTL central European history of much of the former Habsburg Empire, that particular ethnicity had it far rougher while transitioning into modernity, and in my timeline they gain a lot more serious respect and acceptance decades earlier.
Though post-A-H nationalism doesn't entirely go away, it becomes a lot more tempered than in OTL. People's focus on loyalties to their home regions contribute to defanging it somewhat. Without a longer-lasting and destructive fascist or communist occupation of these countries, many post-A-H countries gain independence sooner, get rid of autocracy sooner and get to learn the ropes of democracy sooner and for a much longer time, making them more stable countries and less likely to become victims of political whims. Going back to minorities, including religious ones, I often have to wonder what the experience of the Greek Catholic Church in central Europe would be, given that its members were persecuted and outright banned by communist governments in the central European puppets of the USSR. No joke, Greek Catholicism could only make an official comeback in the early 1990s. You might not guess the GCC had it so rough in the not too distant past, based on its current healthy state, but at one point, its persecutors were intent on driving it into extinction within the former countries of A-H.
Impossible to let them identify as Habsburgs. Citizens of the Habsburg monarchy, a monarchy they can have unironic and honest pride in, that's a little more plausible. Any sort of civic nationalism would be a complex thing to build, though, and Austria-Hungary would have to undergo a huge amount of reform to account for all its constituent nationalities and religious groups. It's hard to compare a continuing A-H to any
contemporary OTL democratic country, with the possible exception of India (multiethnic and multicultural since time immemorial) or Canada (based on a lot of well-working multiculturalism, even if an imperfect one), but both of those examples had also developed in vastly different historical contexts.
Trust me, the average towns and cities of Austria-Hungary were fairly cosmopolitan to begin with.