Die Gute kocht eine Suppe.

Does this have the connotation that it does in English, of like, implying that the woman here is of lower socioeconomic status, sort of like the “help”? In English this would often come across as condescending or insulting towards the woman for this reason, and I’m curious if it has this connotation in German too.

That depends on context, but in almost all cases there wouldn’t be such a connotation. It is possible but it would have to be evident in an explicit way from the context.

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