AX Agent: 실행 이벤트 세션 변이 경로 엔진으로 통합

- ChatWindow에 중복돼 있던 실행 이벤트/Agent run 교차 탭 복원 로직을 AxAgentExecutionEngine helper로 이동함

- AppendExecutionEvent, AppendAgentRun이 공통 session mutation 경로를 사용하도록 정리해 이후 runtime state 공통화 기반을 마련함

- README와 DEVELOPMENT 문서에 2026-04-05 15:42 (KST) 기준 변경 이력 반영

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

docs/DEVELOPMENT.md

@@ -2,6 +2,8 @@
 
 - Document update: 2026-04-05 15:34 (KST) - Rebased the AX Agent improvement plan on actual `claw-code` runtime files instead of prior AX snapshots. The active reference spine is `src/bootstrap/state.ts -> src/bridge/initReplBridge.ts -> src/bridge/sessionRunner.ts -> src/screens/REPL.tsx -> src/components/Messages.tsx -> src/components/StatusLine.tsx`.
 - Document update: 2026-04-05 15:34 (KST) - Locked the AX implementation order to the same quality sequence used by that spine: runtime state canonicalization, prepared execution unification, loop event normalization, timeline render parity, composer/status strip simplification, and recovery/resume validation.
+- Document update: 2026-04-05 15:42 (KST) - Moved the cross-tab conversation restoration path for execution events and agent-run history from `ChatWindow.xaml.cs` into `AxAgentExecutionEngine`. `AppendExecutionEvent` and `AppendAgentRun` now go through one engine-owned session mutation helper, which preserves the active tab conversation while updating the target tab timeline.
+- Document update: 2026-04-05 15:42 (KST) - Verified the first runtime-state/common-engine step with `dotnet build src/AxCopilot/AxCopilot.csproj -c Release -v minimal -p:OutputPath=bin\\verify\\ -p:IntermediateOutputPath=obj\\verify\\` and confirmed warning 0 / error 0.
 - Document update: 2026-04-05 07:11 (KST) - Simplified the AX Agent footer for Cowork/Code by removing the duplicated `MoodIconPanel` chip group from those tabs and leaving workspace context only in the main folder path row. Also removed the outline border from the data-usage button so the footer option strip reads flatter and less pill-heavy.
 - Document update: 2026-04-05 07:08 (KST) - Improved AX Agent responsiveness in three hot paths: added an ordered meta cache in `ChatStorageService` so repeated conversation-list refreshes stop re-sorting the full meta set every time, short-circuited `SaveConversationSettings()` when permission/data-usage/mood/output-format values are unchanged, and debounced the sidebar conversation search refresh to avoid re-filtering on every keystroke.
 - Document update: 2026-04-05 02:00 (KST) - Reworked the AX Agent in-chat gear overlay navigation itself to match the restored internal settings taxonomy: `basic / chat / cowork / code / dev / tools / skill-block`. The left nav labels now follow that scheme, and the overlay rows/toggles are regrouped per tab instead of the earlier `common / service / permission / advanced` split.