gog2002x: I think of Library as "containing" my owned list of games, hence why I was a bit confused by that sentence, since I've never heard anyone call the Library an "owned games folder" before. :)
In Galaxy the button is actually labeled "owned games".
I can only assume that the OP has an additional filter active.
@OP
Try to download the offline installers from this webpage.
Hover the mouse over your profile name on top of this page, then select "games"
All your games should show there.
If they don't, you need to contact support.
But if they do, you can download the installers there and install the games manually without Galaxy, if you want it (they will work with Galaxy, it's just a different installation method).
But You can completely bypass Galaxy anyway. All games also work without it.