the antagonism of Austria and Prussia was not existential, but was for control of the German Confederation
even the antagonism of Austria and Turkey was just a normal border conflict between civilizations
the Entente's opposition to the Central Powers was something totally different. The basic opposition was to the last remnants of the Traditional order in European civilization, which was so overwhelming in the Entente that Wilson for example can't even bring himself to find the overthrow of his erstwhile ally Russia's Tsarist government with a literal communist revolution. This was because the Entente basically held the same sort of revolutionary fervor directed against historical European Monarchism.
That revolutionary antagonism is beyond any normal historically-conditioned antagonism since it basically seeks to bring an end to history. Its expression is one of existential hate for the old order, for the countries which are its representatives, and for the people who still experience life in a Traditional mode of existence, or who wish to do so.
Under these circumstances it's no wonder the Prussians, Austrians, and Turks worked together, and the biggest cuck of the war is clearly the Tsarist regime which undermined itself economically and ideologically through its very engagement in the conflict. This perspective also clearly demonstrates why the great tensions in the Central Powers didn't prevent the alliance from forming, but why Italy found itself betraying the Triple Alliance. The opposition Italy had with Austria was based on liberal nationalism, and even though they were a monarchy their state was correctly identified with modernity. No mere alliance-on-paper could overcome this fundamental opposition, and so it was inevitable that Italy would betray the Triple Alliance the moment it was tested.