Rxxz_935: Someone else confirmed you need GOG Galaxy 2.0.29 in order to get the overlay working and screenshots with F12.
In the meantime you can use photomode on the game and it saves the pictures on your D:\YourUser\Pictures\Cyberpunk 2077 folder.
Edit. I also have 2.0.28.2 so I'm not able to use the overlay yet but it probably will be released in a few days.
I'm on 2.0.30 and it doesn't work for me either. I did F12 about a dozen times in-game last night, checked just now, and I don't have a folder for Cyberpunk 2077, which as far as I understand should be here: C:\Users\%USER%\Documents\GOG Galaxy\Screenshots. I even have a few others games' folders in there from a few months ago.