The Austrian empire itself had too many nationalities/ethnicities in itself and was quickly decaying. It seems obvious that it could not last in its current state. The main part of Austria itself was a German state that was excluded from the unification. There is no question that the Austrians think they are part of greater Germany (as evidenced by naming themselves the Republic of German Austria after WW1, making the allies forbid them from joining Germany).
It seems logical that a great politician and manipulator like Bismarck would try to orchestrate things to weaken and split the Austrian empire (maybe with help from the Hungarians, Slovenians, et al), then absorb the German part into a unified Germany. Also seems like a more natural state for German nationalists.
First of all, the Austrian Empire was not in as much of decay as you propose in my mind. They managed to survive the economical turmoil of the Long Depression from 1873 onwards and absorbed Bosina-Herzegovina. It took more than 4 years of extremely bloody war, multiple disastrous setbacks and 80% casualties in their armed forces until the state actually collapsed.
That said, Bismarck and those that wanted to unite Germany were not German nationalists. They were Prussian nationalists. They wanted a protestant Germany led by and dominated by Prussia. A German Empire that included the German-speaking parts of Austria (Türol, Austria, Sudet, northern Slovenia and so on) would be majority catholic, and would include their Austrian rivals for the leadership of Germany to organise any catholic opposition to Prussian and protestant leadership.
Engineering the split of Austria might not be as easy as you think - the Poles, the Slovenes, the Czechs and the Croatians were mostly loyal to the Austrian Empire during the timeframe. The Romanians in Transylvania had also shown that they would side with the Empire against Hungarian revolters 1848.
Another factor is that of Russia - splitting up the Austrian Empire would create a lot of small states too weak to resist any Russian advanced on the Balkans. The southern border of this German Empire would then be unsecure and volatile, causing multiple problems for the new nation.
In short, Bismarck and those that drove German unification did not want a majority catholic state, did not want their opposition within that state for the catholics to unite behind, considered Austria useful for controlling central Europe and the Balkans and as a friendly neighbour.
For the most part, it is a question of rivalry and superiority in the united country that would be formed. The German Confederation didn't include Austria since its formation in 1815. Another problem were territorial disputed and wars that Prussia and Austria had. Prussia and Austria engaged in war with Denmark in 1864. and took away the province of Schleswig-Holstein. The rivalry at this moment was searing and Prussia and Austria were now at war, which ended in the famous battle of Königgrätz. In the treaty of Prague, Prussia received the territories gained in the war against Denmark. Not long after, the Franco-Prussian war began, the North-German Confederation was formed, effectively moving Austria away from a status of leadership in the unification it had in the past.