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/app/(tabs)/chat.tsx

@@ -13,7 +13,11 @@ import Header from "../../components/Header";
 import BaseBackground from "../../components/BaseBackground";
 import { FlashList } from "@shopify/flash-list";
 import { ChatService } from "../../services";
-import { useChatStore, chatMessageToMessageData, MessageData } from "../../stores";
+import {
+  useChatStore,
+  chatMessageToMessageData,
+  MessageData,
+} from "../../stores";
 import { ProposedEventChange } from "@caldav/shared";
 import { ProposedEventCard } from "../../components/ProposedEventCard";
 

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] }));

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";