It is a bit more complex than that.
Before the Franks came to dominate the rest of the Germans, there were several Stem Duchies; Alemannic, Bavarian, Saxon etc.
The Austrians, non Voralberg, are descendants of Bavarians who themselves were a mixed tribal confederation containing Celts etc. but dominated by Germanic tribesmen. Austria started off as a March which Bavarians settled hence why the Bavarian dialect is spoken in most of Austria, Alemannic Voralberg being the exception. There is no difference between a Bavarian proper and an Austrian particularly in the areas where Central Bavarian is spoken. Slavic influence is greater in Carinthia and obviously Vienna due to its historical multicultural status during the Hapsburg Empire. Nonetheless, the Austrians are no less German than other Germans in the borderlands. Even the West Germans you referenced, to a lesser extent, assimilated others and had a two tier society. The Franks, ancestors of Dutch and Ripurian Franks, assimilated Celts and Roman citizens in the lands that they expanded into. So did Western Alemannic Germans in Switzerland, Alsace etc. The purest, or closest population to ancient West Germans, would probably be North-Western Saxons, Frisians and some of the Dutch in the Northern Lowlands. Probably some English too in Eastern England, East Anglia, who do not have much Celtic ancestry.
As for Eastern Germany, the land stretching all the way to Konigsberg before WW2, it was formed when the Saxons expanded into the Slavic territories of the Wends, Sorbs, Pomeranian Slavs, and Baltic Prussians who were assimilated during the Teutonic Crusades against pagan Balts. However, despite the Germanisation of the above groups, a lot of current East Germans/East Saxons/Prussians descend from ethnic Germans who were brought into these conquered territories as settlers, artisans, clergy, administrators etc.
It is ironic though that the two greatest German States, Austria and Prussia, in the past 500 years have been those that came about due to Historical German expansion East. I read a first person account of the War in the Eastern front from a German soldier's perspective. In it, he spoke of a scene where a Southern German from Lake Constance was being mocked by a fair headed Prussian for his 'non-Aryan' appearance. The Prussian himself might have been a descendant of the 'Aryan' looking Balts who were assimilated by the Saxons. Bloody Humanity!