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/services/interfaces/EventRepository.ts

@@ -8,6 +8,7 @@ export interface EventRepository {
     startDate: Date,
     endDate: Date,
   ): Promise<CalendarEvent[]>;
+  searchByTitle(userId: string, query: string): Promise<CalendarEvent[]>;
   create(userId: string, data: CreateEventDTO): Promise<CalendarEvent>;
   update(id: string, data: UpdateEventDTO): Promise<CalendarEvent | null>;
   delete(id: string): Promise<boolean>;