>>14192081but they were part of the German Confederation
They just were not part of the Revolutionary German Empire, what you are probably thinking of.
The Austrian Monarchy just rejected the claim of the Frankfurt Parliament to be the representative of the German nation. Austria would continue to lead the German nation until the late 1860s when the German War occured.
They did not betray the German nation yet, that betrayal only occured after the second world war with the fabrication of the Austrian pseudo-nation and the fabrication of the legend of Austria being the victim of Nazism.