AX Agent 사이드바 상호작용 프레젠테이션 분리 및 구조 개선 후속 정리

- ChatWindow에서 검색/새 대화 사이드바 interaction을 SidebarInteractionPresentation partial로 분리
- 검색 열기/닫기 애니메이션과 hover 상태 변경을 메인 창 orchestration 코드 밖으로 이동
- README와 DEVELOPMENT 문서에 2026-04-06 11:03 (KST) 기준 구조 개선 완료 범위와 남은 후속 작업 수준 반영
- dotnet build 검증 경고 0, 오류 0 확인

docs/DEVELOPMENT.md

@@ -4931,3 +4931,5 @@ ow + toggle ?쒓컖 ?몄뼱濡??ㅼ떆 ?뺣젹?덈떎.
 - Document update: 2026-04-06 10:44 (KST) - This consolidates timeline-related helpers in one place and leaves the main chat window file with less transcript-specific rendering logic around `RenderMessages()`.
 - Document update: 2026-04-06 10:56 (KST) - Split conversation-management interactions out of `ChatWindow.xaml.cs` into `ChatWindow.ConversationManagementPresentation.cs`. Inline title editing and the conversation action popup (pin/unpin, rename, category change, delete) now live in a dedicated presentation partial.
 - Document update: 2026-04-06 10:56 (KST) - With this pass, the remaining large structure-improvement track is effectively complete; follow-up work is now mostly UX polish and surface-level tuning rather than further decomposition of the main chat window orchestration file.
+- Document update: 2026-04-06 11:03 (KST) - Split sidebar search/new-chat interactions out of `ChatWindow.xaml.cs` into `ChatWindow.SidebarInteractionPresentation.cs`. Hover state changes, sidebar search open/close transitions, and new-chat trigger behavior now live in a dedicated presentation partial.
+- Document update: 2026-04-06 11:03 (KST) - This leaves the main chat window even more orchestration-focused and effectively closes the last obvious sidebar interaction block from the large structure-improvement plan. Remaining work is now follow-up UX polish rather than major decomposition.