Where Do GUI Errors Go Now?

When running a GUI on X11, there is a file called ~/.xsession-errors,
which is basically the destination for stderr for all programs launched
from the GUI. So any error messages they output can be viewed here.

There can be quite a lot of clutter here. Also it’s amazing to see GUI
toolkits report “critical” errors during normal execution of some apps.
But this can also be useful for troubleshooting. Like the time a user
reported trouble with some display function in a proprietary app (I foget
which) after an upgrade to a new machine. I got in and watched as he went
through the steps, and soon saw an error message that it was trying to
launch xfig, which was not found.

It only took a minute to install that package, ask him to try again, and
confirm that it worked.

But anyway, seems there is no equivalent in Wayland-based GUIs. Does
stderr from a GUI-launched app just get thrown away now?