refactor(layout): extract AppNavbar component and rewrite app.vue (F7.3)

Extract 680-line navbar into LayoutAppNavbar component with useNavDropdown
composable. app.vue reduced from 698 to 22 LOC.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/composables/useNavDropdown.ts

@@ -0,0 +1,65 @@
+import { ref, watch, onUnmounted } from 'vue'
+import { useRoute } from '#imports'
+
+export function useNavDropdown() {
+  const openDropdown = ref<string | null>(null)
+  let dropdownCloseTimer: ReturnType<typeof setTimeout> | null = null
+  const route = useRoute()
+
+  const setDropdown = (name: string) => {
+    if (dropdownCloseTimer) {
+      clearTimeout(dropdownCloseTimer)
+      dropdownCloseTimer = null
+    }
+    if (openDropdown.value !== name) {
+      openDropdown.value = name
+    }
+  }
+
+  const scheduleDropdownClose = (name: string) => {
+    if (dropdownCloseTimer) {
+      clearTimeout(dropdownCloseTimer)
+    }
+    dropdownCloseTimer = setTimeout(() => {
+      if (openDropdown.value === name) {
+        openDropdown.value = null
+      }
+      dropdownCloseTimer = null
+    }, 200)
+  }
+
+  const closeDropdownNow = () => {
+    if (dropdownCloseTimer) {
+      clearTimeout(dropdownCloseTimer)
+      dropdownCloseTimer = null
+    }
+    openDropdown.value = null
+  }
+
+  const toggleDropdown = (name: string) => {
+    if (openDropdown.value === name) {
+      closeDropdownNow()
+      return
+    }
+    setDropdown(name)
+  }
+
+  watch(() => route.fullPath, () => {
+    closeDropdownNow()
+  })
+
+  onUnmounted(() => {
+    if (dropdownCloseTimer) {
+      clearTimeout(dropdownCloseTimer)
+      dropdownCloseTimer = null
+    }
+  })
+
+  return {
+    openDropdown,
+    setDropdown,
+    scheduleDropdownClose,
+    closeDropdownNow,
+    toggleDropdown,
+  }
+}