MasterZoen: Well, I finally figured out why I had no overlay and never had any notifications pop up: I didn't have Public Beta ticked in the General tab of Galaxy Settings. The notifications and overlay are beta features, so if you have beta features disabled then you don't see them. It would have been nice if that were actually mentioned somewhere on the Game Features tab... I hope this will fix the problem.
Now Galaxy just needs to realize that I filled all my cybernetic slots two days ago...
Edit:
So, this enabled desktop notifications, and the overlay is now active in some games, but I can't enable it in Cyberpunk 2077 and several other games that list support for it.
Edit 2:
Uninstalling and reinstalling the game fixed the issues.
I have this problem with the achievements and I've updated to beta. I don't want to have to uninstall the game as my internet is incredibly slow. Is there another way around this? No achievements have unlocked for me at all but it is tracking my time played.