Mozart was Austrian though, born in Salzburg, even though Salzburg was only incorporated to Austria after his death, but it was always more tied to Austria than Germany.
True, but I think the fact that Salzburg was technically a different polity than the archduchy of Austria is what the saying refers to. I might be misremembering it and it might actually be Beethoven though
Well Mozart himself probably did consider himself German in broader and probably rather cultural sense, especially that he lived before the rise of modern idea of nation when that question was redefined to what we mean today. Not to mention Austria was always somewhat peculiar about it too.