I've always known
Emily was the female form of
Emil, which comes from Aemilius which is a Latin and not Germanic name. So saying it comes from Old
German is news to me. I've never heard about it coming from
Amelia or
Amalia, which anyway comes from a word meaning "work" , which is not the same as saying it means "industrious worker".
It looks like you've picked your definition from a baby name book. These are not always very reliable and try to make sure that all names mean something nice and pretty, which isn't always the case.
"Ever tried. Ever failed. No matter. Try Again. Fail again. Fail better"-Samuel Beckett