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/ChatStore.ts

@@ -23,7 +23,7 @@ interface ChatState {
 export const useChatStore = create<ChatState>((set) => ({
   messages: [],
   addMessages(messages) {
-    set((state) => ({messages: [...state.messages, ...messages]}))
+    set((state) => ({ messages: [...state.messages, ...messages] }));
   },
   addMessage: (message: MessageData) => {
     set((state) => ({ messages: [...state.messages, message] }));