To be honest, as a German I have no idea where this increase in productivity is supposed to have occurred. My experience and intuition is that Germany is suffering from a rise in lethargy and inefficiency ("German efficiency" is a meme that's utterly outdated and inapplicable, at least in my sector, IT).
I'd be happy to learn about concrete and representative information that balances my perspective but I have yet to see it.
Production is the gross output. Productivity is production divided by the whole population or the working population.
You can easily have a situation were production shrinks but productivity is unchanged, e.g. because a cohort leaves the workforce and becomes pensioneers.
I guess the truth lies somewhere in the middle.