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/src/app.ts

@@ -10,7 +10,7 @@ import {
   MongoEventRepository,
   MongoChatRepository,
 } from "./repositories";
-import { ClaudeAdapter } from "./ai";
+import { GPTAdapter } from "./ai";
 
 const app = express();
 const port = process.env.PORT || 3000;
@@ -43,7 +43,7 @@ const eventRepo = new MongoEventRepository();
 const chatRepo = new MongoChatRepository();
 
 // Initialize AI provider
-const aiProvider = new ClaudeAdapter();
+const aiProvider = new GPTAdapter();
 
 // Initialize services
 const authService = new AuthService(userRepo);