AX Agent 선택 팝업 렌더를 분리해 footer 선택 UX 구조를 정리한다

- ChatWindow.SelectionPopupPresentation.cs를 추가해 워크트리 선택 팝업과 공통 선택 row 렌더를 메인 창 코드 밖으로 이동했다.

- ChatWindow.xaml.cs에서 작업 위치 선택 팝업 조립 책임을 제거해 대화 상태와 세션 orchestration 중심 구조를 더 선명하게 만들었다.

- README와 DEVELOPMENT 문서에 2026-04-06 09:14 (KST) 기준 구조 분리 이력을 반영했다.

- dotnet build src/AxCopilot/AxCopilot.csproj -c Release -v minimal -p:OutputPath=bin\\verify\\ -p:IntermediateOutputPath=obj\\verify\\ 검증 결과 경고 0 / 오류 0을 확인했다.

docs/DEVELOPMENT.md

@@ -1,5 +1,8 @@
 # AX Copilot - 媛쒕컻 臾몄꽌
 
+- Document update: 2026-04-06 09:14 (KST) - Split worktree-selection popup rendering into `ChatWindow.SelectionPopupPresentation.cs`. The current workspace/worktree chooser and the shared selected-row popup card renderer now live outside `ChatWindow.xaml.cs`, reducing footer selection UI density in the main window file.
+- Document update: 2026-04-06 09:14 (KST) - This keeps branch/worktree/footer chooser UX on the same presentation side of the codebase and leaves the main chat window more focused on runtime orchestration and conversation flow.
+
 - Document update: 2026-04-06 09:03 (KST) - Split common themed popup construction out of `ChatWindow.xaml.cs` into `ChatWindow.PopupPresentation.cs`. Shared popup container creation, generic popup menu items/separators, and the recent-folder context menu now live in a dedicated partial instead of the main window orchestration file.
 - Document update: 2026-04-06 09:03 (KST) - This keeps footer/file-browser popup styling on a single visual path and reduces direct popup composition inside the main chat window flow, making further `claw-code` style popup UX work easier to maintain.