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>

package.json

@@ -0,0 +1,20 @@
+{
+  "name": "brainstorming",
+  "private": true,
+  "type": "module",
+  "scripts": {
+    "dev": "nuxt dev",
+    "build": "nuxt build",
+    "preview": "nuxt preview"
+  },
+  "dependencies": {
+    "better-sqlite3": "^11.9.1",
+    "nuxt": "^3.17.2",
+    "@nuxt/ui": "^3.1.3"
+  },
+  "devDependencies": {
+    "@types/better-sqlite3": "^7.6.13",
+    "typescript": "^5.8.3"
+  },
+  "packageManager": "pnpm@10.11.0"
+}