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>

server/api/auth/logout.post.ts

@@ -0,0 +1,8 @@
+import { destroySession } from '../../utils/auth'
+
+export default defineEventHandler((event) => {
+  const token = getCookie(event, 'session')
+  if (token) destroySession(token)
+  deleteCookie(event, 'session', { path: '/' })
+  return { ok: true }
+})