carrioncrow I also was able to install play services when I first installed GOS but the option is now gone for me.
muhomorr I am currently running Android 12 SP2A.220505.008. I will try to update, but when I click the "check for updates" button in settings it first gives me a notification which says:
"Downloading system update"
Then it changes to
"Installing system update"
However the progress bar does not move and the notification dissapears soon after.