I got a popup about an update, but I was in the middle of the cyberpunk update and so I picked "update later" but then the popup never appeared again. How do I make the popup appear or something? :D

restart the client and wait

that's what I did multiple times with no result

When I had issues with automatic updates, I just used the offline installer to update.
https://remote-config.gog.com/components/webinstaller?component_version=2.0.0

there is no way to tell Galaxy to update itself... yes that is fucked up but what can you do?
the offline installer page Ice-mage points to only has one copy of Galaxy and it's not always upgraded to show the lastest but it does at least give you some control

goto Galaxy settings to check if your build version is lower than what is offered online & if it is then download the installer [run it as admin when you actually install it]