feat: initial brainstorming app — Nuxt 3 + SQLite + admin auth

Nuxt 3 app with:
- SQLite (better-sqlite3) for persistence
- Anonymous idea submission and voting
- Admin auth with session cookies
- AI analysis via Gemini API
- Nuxt UI components + Tailwind

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

app/composables/useAuth.ts

@@ -0,0 +1,20 @@
+export function useAuth() {
+  const admin = useState('admin', () => false)
+
+  async function check() {
+    const data = await $fetch('/api/auth/me')
+    admin.value = data.admin
+  }
+
+  async function login(password: string) {
+    await $fetch('/api/auth/login', { method: 'POST', body: { password } })
+    admin.value = true
+  }
+
+  async function logout() {
+    await $fetch('/api/auth/logout', { method: 'POST' })
+    admin.value = false
+  }
+
+  return { admin, check, login, logout }
+}