feat: replace Claude with GPT for AI chat integration

- Replace ClaudeAdapter with GPTAdapter using OpenAI GPT (gpt-5-mini)
- Implement function calling for calendar operations (getDay, proposeCreate/Update/Delete, searchEvents)
- Add provider-agnostic AI utilities in ai/utils/ (systemPrompt, toolDefinitions, toolExecutor, eventFormatter)
- Add USE_TEST_RESPONSES env var to toggle between real AI and test responses
- Switch ChatService.processMessage to use real AI provider
- Add npm run format command for Prettier
- Update CLAUDE.md with new architecture

package.json

@@ -6,6 +6,9 @@
     "apps/*",
     "packages/*"
   ],
+  "scripts": {
+    "format": "prettier --write \"apps/*/src/**/*.{ts,tsx}\" \"packages/*/src/**/*.ts\""
+  },
   "devDependencies": {
     "eslint": "^9.25.0",
     "prettier": "^3.7.4",