The prussians lose the 1866 war, lose many/all of the "western" posessions and are kicked out of the German Federation -
I'm assuming you mean the German Confederation, which itself ended in 1866 as a result of collapsing from the War.
50 years later the Prussians are Prussians and NOT Germans. Just the same as Austrians today think the are Austrians first and just speak German language.
The seperate Austrian identity came about as a very specific situation, that is the leaders did'nt want to be lumped in with the rest of Germany in being punished and so they made-up an identity after the war to convince the Allies they were'nt to blame and it evolved over time as a result of Austrias position in the Cold War.
Prussia losing the Austro-Prussian war is not going to lead to the same thing.