Themken: I know next to nothing of Galaxy. As you very well know, there is no Linux version of it. But, I think I have read that is also how to find it in Galaxy but for sure there it hides in the games' cards in your library if you use a web browser.
Ever since the beta of the first version of Galaxy and all through 1.x Galaxy's life you haven't been able to view the Serial Keys. It does not display them. You have to view your Library in a web browser to see them.
I'm not actually sure if GOG bothered to display the serials, which are already in the Library page it uses btw, with 2.0 or not. Maybe they even finally patched the 1.x branch recently.
Anyway, you used to have to specify "in a web browser" as Galaxy's 'more' menu lacked that entry.