I noticed that both on the desktop website (Google Chrome) and in the Galaxy client my wishlist doesn't show up. Also my collection doesn't show up in the desktop website.
What's going on? How do I get the website to work properly and show my wishlist and collection?

I'm experiencing the same issue
I just managed to bring my wishlish back by disabling the ad blocker that came integrated into my browser.
I also got back my library, took many more tries so now I'm not completely sure if that was the problem. GOG servers may have gone down for a brief moment. Yeah, I think that's the case, as other features of the site are still running slow or bugging out. The ad blocker thing was probably just a coincidence.

Anyway, all is fine now.

(multiple edits on the same post)