Alright, I can work with that. I did think my POD would be a bit implausible anyway.
So, how does this Germany differ from OTL Germany?
Well we would have a less centralized, less militarized version of the OTL Germany who would be more alike to a modernized centralized and formally hereditary HRE (with the parliament of Frankfurt or another analogue replacing the Imperial Diet). As the Habsburg had already the Imperial title and were the rulers of Germany (at least in name) for centuries neither Prussia, Bavaria or any other state will be able or think to impose restrictions on the use of the Imperial title from the Habsburg (so the Austrian title will be most likely absorbed in the new Imperial title of Germany with the members of the Imperial House most likely know with the double title Princes/Princesses of Germany and Archdukes/Archduchesses of Austria). Maybe the German title can be restricted only to Franz Joseph’s direct descendants but nothing more...
Neither Metternich or Bismarck will have any power in this Germany so I do not know if the ATL Empire of Germany will have a great statesman (and who can be).
Hungary will be independent under King Maximilian, while Bohemia, Trieste, Istria and Dalmatia and most likely Galicia will be part of the German Empire. I do not know what will happen to Lombardy and Venetia (included in the Empire of Germany or another independent kingdom under either FJ’s next brother Archduke Karl Ludwig or the GrandDuke of Tuscany?)
I would also let Franz Joseph marry his first choice bride aka
https://en.m.wikipedia.org/wiki/Princess_Anna_of_Prussia (she was already engaged when he met her OTL but here - unlike OTL were was practically impossible because the tensions between Catholic Austria and Protestant Prussia - breaking her engagement because the Emperor of Germany wanted her would be quite simple as he would have the precedence over a minor German lord, who can be compensated with some kinswoman of FJ like his first cousin Helene of Bavaria).
As Archduchess Sophie was close to her sister Ludovica, the latter second daughter Elisabeth of Bavaria instead will be directly selected as bride for Maximilian, King of Hungary (as Helene was sent in Hesse in place of Anna) and will live happily there free from the Hofburg, Archduchess Sophie’s control and Vienna’s oppressive etiquette.