Layered images are complicated. Split out live to minimal and live for core, even if it doesn't make much sense.

live-build/auto/config

@@ -814,10 +814,11 @@ case $PROJECT in
 		touch config/universe-enabled
 		KERNEL_FLAVOURS='generic-hwe-22.04'
 		PASSES_TO_LAYERS="true"
+		# the minimal layer
+		add_task minimal minimal
 		# the live layer, contains all packages for the live session installer
-		add_task live minimal
+		add_snap minimal.live ubuntu-core-desktop-installer/classic core22 snapd
-		add_snap live ubuntu-core-desktop-installer/classic core22 snapd
+		add_package minimal.live linux-$KERNEL_FLAVOURS plymouth-theme-spinner squashfs-tools snapd cloud-init
-		add_package live linux-$KERNEL_FLAVOURS plymouth-theme-spinner squashfs-tools snapd cloud-init
 
 		# now let's create the neccessary catalog files
 		cat <<-EOF > config/install-sources-in.yaml
@@ -836,7 +837,6 @@ case $PROJECT in
 
 		# we have to manually mark the live layer as the LIVE_PASS, since it's also
 		# the only layer we build
-		LIVE_PASSES="live"
 		;;
 
 	ubuntu-oem)