Presumably Vienna would be the capital of an Austrian kingdom inside the federal German Empire, akin to Munich as being that of Bavaria. So, it's not going to fall into dishevelment or irrelevance, though not all that many diplomats or royals will be going there in comparison to the past.
It will retain the monuments to its former glories, and people will still be proud to be Viennese - after all people are proud to come from Leeds or Liverpool in the UK, it's not a requirement for where you live to have political importance.
Presumably, akin to Bavaria, Saxony and Wurrtemburg, Austria would have its own peace-time army, and presumably Hapsburg Archdukes could still rise to high command levels in the unified Imperial Army based on competence, akin to Prince Leopold of Bavaria
There might well be a formal merger of Catholic conservative parties between the Austrian and Bavarian ones.
Damn, the barmaid is threatening to take my dinner away cos I am typing!