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

apps/server/package.json

@@ -8,13 +8,13 @@
     "start": "node dist/app.js"
   },
   "dependencies": {
-    "@anthropic-ai/sdk": "^0.71.2",
     "@caldav/shared": "*",
     "bcrypt": "^6.0.0",
     "dotenv": "^16.4.7",
     "express": "^5.2.1",
     "jsonwebtoken": "^9.0.3",
     "mongoose": "^9.1.1",
+    "openai": "^6.15.0",
     "rrule": "^2.8.1"
   },
   "devDependencies": {