Does that also mean that Germans have to apply for new license plates when moving from one district to another, or does the license plate only refer to the district of original purchase?
In Poland you have to get a new license plate every time the car changes its owner, unless they happen to live in the same city. But the first 2-3 letters change depending on where you live, and it's quite granular, so even if you sell your car to a city not far away it might need a new license plate.
From other places where this holds, it only refers to the district of the original purchase. And people don't move that much either, so 90% of the plates or such are accurate as to their owner's district too.