@trainerjack Apparently, the codes were used to pull up scans of the artwork on a Japanese mobile app called Pokémon Hiroba (aka Pokémon Square or Pokémon Plaza). Some more info about that can be found here and here. This info was first shared by @witchery in this thread in 2022: Any other way to use the ex serial code?. Before that, I didn’t even know where the codes were used for at all.
As for why there are different codes. Why the Commons have four codes and Uncommons two codes in Japanese; and Commons have three codes and Uncommons and Energies two codes in other languages; why the English EX Emerald Uncommons have only a single code, whereas German/French/Italian/Portuguese Uncommons from that set have two codes; etc. I honestly don’t know. I’m not even sure if the codes on the international cards would work on that Japanese Pokémon Square/Plaza mobile app, and if not, I have no idea why the international cards even have codes to begin with…
Overall there’s still a lot of mystery surrounding the EX era codes. But to quote the first Japanese blog I posted, their main purpose is to:
当時はコレクター泣かせなコレクター要素の1つで多くの（コアな）コレクターがコンプリートするのに必死になっていました。
At that time, it was one of the collector’s items that made collectors cry, and many (core) collectors were desperate to complete it.
Greetz,
Quuador