AX Agent 대화 목록 필터 프레젠테이션 분리 및 사이드바 구조 정리

- ChatWindow에서 대화 목록 필터/정렬 interaction과 선호 저장 로직을 ConversationFilterPresentation partial로 분리
- 실행 중 보기, 최근/활동 정렬, 관련 버튼 UI 갱신을 메인 창 orchestration 코드 밖으로 이동
- README와 DEVELOPMENT 문서에 2026-04-06 11:11 (KST) 기준 구조 개선 누적 완료 범위 반영
- dotnet build 검증 경고 0, 오류 0 확인

docs/DEVELOPMENT.md

@@ -4933,3 +4933,5 @@ ow + toggle ?쒓컖 ?몄뼱濡??ㅼ떆 ?뺣젹?덈떎.
 - 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.
+- Document update: 2026-04-06 11:11 (KST) - Split conversation list filter/sort interactions and preference persistence out of `ChatWindow.xaml.cs` into `ChatWindow.ConversationFilterPresentation.cs`. Running-only toggles, recent/activity sort toggles, UI-state refresh, and conversation-list preference apply/persist logic now live in a dedicated presentation partial.
+- Document update: 2026-04-06 11:11 (KST) - This keeps sidebar state presentation more cohesive and further narrows the main chat window file toward orchestration-only responsibilities. Remaining work is now post-plan polish rather than another major structural split.