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/client/src/stores/index.ts

@@ -1,3 +1,7 @@
 export { useAuthStore } from "./AuthStore";
-export { useChatStore, chatMessageToMessageData, type MessageData } from "./ChatStore";
+export {
+  useChatStore,
+  chatMessageToMessageData,
+  type MessageData,
+} from "./ChatStore";
 export { useEventsStore } from "./EventsStore";