The author calls Austria a German state just like Bavaria.

Austria is basically the German-speaking part of the former Austro-Hungarian Empire. It was even briefly called the "Republic of German-Austria" after the empire's dissolution in 1918: https://en.wikipedia.org/wiki/Republic_of_German-Austria

Because Austria was a German state. We are talking 1920, mind. A national Austrian identity separate from the wider German one did not develop until after the second world war.

Austria was an independent empire which was only dissolved in 1918. It existed before the unification of Germany.

Germany wasn't a country before 1871. However, Germany existed as a cultural region. Austria was always considered to be a part of Germany, even the leading part. When Germany united, there were two options, the small-Germany (kleindeutsche) and large-Germany (großdeutsche) solution, the latter including either the whole Austrian empire or just the German-speaking parts in the unified country. The reason why this did not come to pass was that Bismarck and the Prussian rulers (Hohenzollern) wanted to control Germany, not share the rule with the competing Habsburh family, the rulers of Austria-Hungary.

Let's not forget that WWI ended two years before and was started from Vienna, Austria. Making it a center of new Europe has a certain stink to it.