Worldwide collection
so I assume they release new coins from one mint until all the stocks from one mint are used up before moving to the next one.
No, that is not how this is done. Various mints release new coins (almost) at the same time. It's about demand. More importantly, it's a regional thing. For example. It's more likely to find new coins from the Berlin mint (mintmark ‘’A'') in the eastern parts of Germany; coins from Munich mint in the south-east, and coins from Stuttgart (''F'') and Karlsruhe (''G'') in the western and middle parts of Germany. However, this is a generalisation. So, yes, I have found new coins with mintmark ‘’D'' or ‘’J'' where I live (western part of Germany).
This is Germany which means it's “complicated.”
I think the Bundesbank used the 2002 date for some unknown reasons becuase it is highly likely most of the 2002 dated coins were minted prior to 2002 probably as early as 1999 like what Ireland, Portugal among other countries that didnt put the acual year of minting.
The Bundesbank used the date “2002” because it was the year the Euro coins and banknotes were issued. Of course, minting of these coins began in 1999. So, yes, Bundesbank did what Italy, Ireland and Portgual and others did in contrast to France, Finland, Netherlands, Belgium, Spain where the year of minting is on the coins.