I am able to wishlist on the browser, but on the application I can't wishlist a game. If I try to wishlist, I would be sent a code to put into the two-factor authentication, but once I put the code it tells me "We're overwhelmed by the popularity of our service. Please check back soon."

I cannot understand why people insist on using Galaxy while it is still so broken.

Try using your regular browser to wishlist, or perhaps send a support ticket to Gog(via the regular browser as well, as I hear it works better) asking them if the service(2fa) is overloaded or if it's a bug. You could also disable 2fa temporarily to wishlist things, and then re-enable it, but that might be too risky/too much work.

Gl, at any rate.