The German tax system can be complex at times, especially regarding foreign income because Germany taxes their residents based on their "world-wide" income.
Based on the DBA (the tax treaty) between the U.S. and Germany, more specifically §19(3), VA disability compensation is tax free in Germany. However, under §23(3)a, Germany "retains the right" to use any income that is excluded from direct taxation noted in the treaty towards their 'rate of tax' (in German, the "Progressionsvorbehalt") to determine one's overall tax bracket. In other other words, 'in-diect' taxing of income by raising one's taxable income level!
However, before the German "Finanzamt" can do this, they must under German tax law determine the type of income they are dealing with because there are only certain, limited types of income that can be applied toward the "Progressionsvorbehalt." So under German tax law VA disability compensation is characterized as income falling under §3 Nr. 6 EStG. This type of income is not specifically listed under §32b EStG (which is the tax law pertaining to the "Progressionsvorbehalt'), and therefore cannot also be applied to it! VA disability compensation is tax free in Germany and cannot be applied to their progressive tax law either! Below you'll find the DBA bewteen the U.S. and Germany, and an article written -in German- by a tax expert specializing in foreign income under German tax law. I have also attached an excerpt from a legal newsletter from 2018 from a German Lawyer who works for EUCOM that also states VA compensation is not taxable in Germany, and doesn't fall under their progressive tax rate either. He also states VA compensation doesn't even need to be reported to the German tax authorities!
Based on the DBA (tax treaty) bewteen the U.S. and Austria, more specifically §19(1) VA compensation is tax free in Austria. However, under §22 it appears Austria may 'retain the right' be able to use any tax free income in Austria toward their Progressive tax (the "Progressionsvorbehalt") as well.
However, Austria is required by their tax law to determine the type of income that is derived from a foreign source. It appears that VA disability comepnsation would fall under §3 EStG (1988) Nr. 1(1). Since the "progressionsvorbehalt" in Austrian tax law is not explicitivily listed, it only appears to be used in certain cases of income under §3 EStG Nr. 2 and 3. Therefore it appears that VA disability compensation is not used under the "progressionsvorbehalt" either.
If you reside in Austria, it would be imperitive that you seek out profession tax advice to determine whether VA comepnsation would be seen as income under §3 Nr. 1(1) EStg (1988) and whether it is exempt from the "progressionsvorbehalt" under §3 Nr. 2 and 3, or whether since it is simply "Ausländische einkünfte" if it would be used under the "progressionsvorbehalt" regardless of the type of income it falls under Austrian tax law. I have included a copy of the U.S.-Austrian tax treaty here for reference.