I think Gnome Software should also handle Gnome Extensions because Gnome Software and Gnome Extensions are Gnome Stuff, KDE Discover handles updates of Plasma extensions, Flatpaks and firmware, but does not suppoer rpm-ostree right now.
I looked at man gnome-extensions and gnome-extensions --help but cannot identify a subcommand to update all installed extensions:
gnome-extensions COMMAND [ARGS…]
help Print help
version Print version
enable Enable extension
disable Disable extension
reset Reset extension
uninstall Uninstall extension
list List extensions
info Show extension info
show Show extension info
prefs Open extension preferences
create Create extension
pack Package extension
install Install extension bundle
The only update related option I found is gnome-extensions list --updates, which seems to list those extension with pending updates, but does not update them.
Did I miss the info how I can update the installed Gnome extensions from the commandline?
Update will update whatever commit you are currently deployed on, including layered packages. Upgrade will upgrade the commit you are currently deployed on including layered packages that need it. Upgrade is the actual command and update is an alias for it within rpm-ostree. Hope that ends the confusion.