feat: scaffold Nuxt 3 + Nuxt UI 3

Initialize Nuxt 4 project with @nuxt/ui template including Tailwind CSS v4,
TypeScript, ESLint, and Nuxt UI v3 (via @nuxt/ui package).

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

front-end/app/components/TemplateMenu.vue

@@ -0,0 +1,49 @@
+<template>
+  <UDropdownMenu
+    v-slot="{ open }"
+    :modal="false"
+    :items="[{
+      label: 'Starter',
+      to: 'https://starter-template.nuxt.dev/',
+      color: 'primary',
+      checked: true,
+      type: 'checkbox'
+    }, {
+      label: 'Landing',
+      to: 'https://landing-template.nuxt.dev/'
+    }, {
+      label: 'Docs',
+      to: 'https://docs-template.nuxt.dev/'
+    }, {
+      label: 'SaaS',
+      to: 'https://saas-template.nuxt.dev/'
+    }, {
+      label: 'Dashboard',
+      to: 'https://dashboard-template.nuxt.dev/'
+    }, {
+      label: 'Chat',
+      to: 'https://chat-template.nuxt.dev/'
+    }, {
+      label: 'Portfolio',
+      to: 'https://portfolio-template.nuxt.dev/'
+    }, {
+      label: 'Changelog',
+      to: 'https://changelog-template.nuxt.dev/'
+    }]"
+    :content="{ align: 'start' }"
+    :ui="{ content: 'min-w-fit' }"
+    size="xs"
+  >
+    <UButton
+      label="Starter"
+      variant="subtle"
+      trailing-icon="i-lucide-chevron-down"
+      size="xs"
+      class="-mb-[6px] font-semibold rounded-full truncate"
+      :class="[open && 'bg-primary/15']"
+      :ui="{
+        trailingIcon: ['transition-transform duration-200', open ? 'rotate-180' : undefined].filter(Boolean).join(' ')
+      }"
+    />
+  </UDropdownMenu>
+</template>