So, GOG Galaxy 2.0 overlay is on in the launcher settings, but the option to turn it on in Cyberpunk 2077 settings is disabled. I didn't expect that to occur since it's a CDPR original game

You should be able to turn it off the overlay entirely in GOG Galaxy, this did make the game last longer for me but there were still crashes.

But I want to turn it on. I just can't do it to Cyberpunk

Oh, so it's not just me then. I though my galaxy was broken or something. Hope they enable it soon.

I had this issue, too, and I had to submit a ticket to find the answer. You have to enable beta versions in GOG Galaxy settings (and then wait for the download prompt because you can't check on demand for some reason) and upgrade to beta version 2.0.31. Once you have that you will be able to enable the overlay in Cyberpunk 2077.

I can't post the link to the support article here but the title of it (if you want to search) is: "Cyberpunk 2077 - GOG GALAXY's Overlay"

Trying the link again: support.gog.com/hc/en-us/articles/360016365497-Cyberpunk-2077-GOG-GALAXY-s-overlay?product=gog