Aha, I think I’ve found it.
Turning on gdm debug shows this:
gdm[9287]: Gdm: GdmManager: session failed to start: GDBus.Error:org.gnome.DisplayManager.SessionWorker.Error.OpeningSession: Failed to execute PostLogin script
gdm[9287]: Gdm: GdmDisplay: Session never registered, failing
The PostLogin script I have seems to be:
#!/bin/sh
#Manjaro tweak to kill double shell
grep -q ^AutomaticLoginEnable=True /etc/gdm/custom.conf || pkill -KILL -u gdm
Deleting this allows me use GDM again!
Looking up the contents of the file brings me to this thread Unable to log in using GDM after Jan. 4 2026 update - #8 by heistp which I completely missed in the hours of searching for any related issues.
Like the user in that thread, I also installed Manjaro for the first time in 2020, so perhaps it only affects users who have fairly long-lived installations. I suppose the ghosts accumulate.