refactor: improve AI event handling and conflict display in chat

- AI fetches events on-demand via callbacks for better efficiency
- Add conflict detection with warning display when proposing overlapping events
- Improve event search and display in chat interface
- Load full chat history for display while limiting AI context

apps/server/src/ai/utils/index.ts

@@ -1,9 +1,4 @@
-export {
-  formatExistingEvents,
-  formatDate,
-  formatTime,
-  formatDateTime,
-} from "./eventFormatter";
+export { formatDate, formatTime, formatDateTime } from "./eventFormatter";
 export { buildSystemPrompt } from "./systemPrompt";
 export {
   TOOL_DEFINITIONS,