feat(SPA): schema list and the sidebar Content group

web/src/components/DirectoryBadge.vue

@@ -4,7 +4,7 @@ import { t } from '@/i18n'
 import { computed } from 'vue'
 
 const props = defineProps<{
-	kind: 'default' | 'noindex' | 'linked' | 'guest'
+	kind: 'default' | 'noindex' | 'linked' | 'guest' | 'builtin'
 }>()
 
 const badges = {
@@ -36,6 +36,13 @@ const badges = {
 		icon: 'i-lucide-user',
 		class: 'border border-accented bg-transparent text-toned',
 	},
+	builtin: {
+		get label() {
+			return t('Built-in')
+		},
+		icon: 'i-lucide-lock',
+		class: 'border border-accented bg-transparent text-toned',
+	},
 } as const
 
 const badge = computed(() => badges[props.kind])