Karl..
A-H was at a rather pivotal moment in its history in 1914. Franz Joseph was in his last years, and the next renewal of the Ausgleich in 1917 was coming up.
Absent the war and its stress, Franz Joseph might have lived a bit longer, so the Ausgleich might have gone fairly smoothly in terms of maintaining the status quo. But what if he dies, say, in 1916, as in OTL? Would A-H have collapsed in the face of Franz Ferdinand's reform proposals and Hungarian opposition?
Actually, Karl was quite the reformer and assuming he succeeds in the ATL in 1916 but in a TL without an ongoing European Conflict, it's possible his own recognition of the need for reform would have been achievable whereas in OTL the War made the peaceful reformation of the Austro-Hungarian Empire impossible.
So Charles I (as we should call him) recalls the Imperial Parliament and offers a full confederation to the peoples of the Empire with full autonomy. Remember, there is no War, no Fourteen Points and no Lansing Note so I think you could argue Charles's reforms would be generally welcome and the Empire would transition to a Confederation by 1920.
The problem of course is once you start giving out power, where do you stop ? The demands would move from autonomy to self-governance to independence and I would think within a generation Vienna would be facing terrorism from any other of violent pro-independence groups such as the Poles, Slovenes, Czechs, Croats, Slovaks and the rest some of whom would be aided and abetted by external powers.
Inevitably, the Austro-Hungarian Empire has two options - to try and maintain the status quo by force or seek a managed dissolution.
It seems reasonable to suppose without exile Charles would have lived beyond 1922 (assassin's bullets and bombs permitting). It's likely he could have lived well into the 1950s or even the 1960s.
Could he have survived as monarch of a Commonwealth of states (on the British model) or were the racial tensions such that separation (managed or otherwise) was the only option ? History dictates a mixture of the two so by 1955 we see the ageing Charles abdicating in favour of his son, Otto, whose remit is now Austria, Slovenia, Bohemia and Moravia. Independent Hungary and Poland along with Croatia are generally friendly but Slovakia less so.