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/app.vue

@@ -0,0 +1,10 @@
+<script setup lang="ts">
+const { check } = useAuth()
+onMounted(() => check())
+</script>
+
+<template>
+  <UApp>
+    <NuxtPage />
+  </UApp>
+</template>