So, how do I start troubleshooting this? I looked in /var/log/gdm3
logs, but couldn't see anything that lept out. There were some errors
from the nvidia driver levels, but those were in older logs and, as I
say, the UI works, it's just not gnome3.
As you do not seem to know what has happened:
You are logged into the "fallback mode", also known as gnome classic. I only know of two reasons, you either (by mistake) chose this as the session in gdm when you logged in, or gnome thinks your 3D graphics support is insufficient.
I would look at the list of recently upgraded packages, anything relating to gnome or graphics drivers.
Unfortunately, I do not know how to troubleshoot it. I assume it would be in some logfile, but as you did not see anything in gdm3, I do not know where you should look.