As a non-native speaker of both English and German, I feel a little difference in usage. I liked this bit of slop:

‘The most significant nuanced departure is that "sonst" can mean "normally," "usually," or "in general," contrasting a specific event against a baseline of normality. "Else" cannot do this.’

There is an etymological root to ‘sonst’ that is also the root of English ‘thus’. The German explanation would fit well in this story (but indeed no evidence presented).