I was using 22.04 LTS out of the box with Nouveau and Wayland. It was working really well (I could even choose to run programs with the integrated GPU or the discrete GPU!), but I had an issue I thought was related to the graphics driver (TLDR: it wasn't).
As part of my troubleshooting I switched to the Nvidia driver. I went to Settings -> About -> Software Updates -> Additional Drivers. From there I checked the box forNVIDIA driver (open kernel) metapackage from nvidia-driver-530-open (proprietary, tested). After restarting and logging in, I noticed my system had switched to X11.
However, now I am no longer using the Nvidia driver. I went back into the Additional Drivers tab and checked the box for Nouveau, but my system is still using X11. In fact, the only Nouveau option now listed there is Nouveau with X.Org (see screenshot below).
I don't have a gear icon at the login screen that lets me choose, as some answers have suggested. Likewise, editing /etc/gdm3/custom.conf and setting WaylandEnable=true does nothing. So right now it seems I'm stuck with X11 and no longer have the graphics card switcher options I had out of the box. It's pretty frustrating that I can't seem to just revert back to the prior settings...
How can I switch back to Wayland?