코드 탭 컨텍스트 영속화와 Auto budget 복구 적용

- AxAgentExecutionEngine에서 시스템 프롬프트 중복을 제거하고 structured tool_use/tool_result 전사본을 conversation.Messages로 동기화해 다음 턴과 저장 이력에서도 코드 작업 컨텍스트가 유지되도록 수정
- AgentQueryContextBuilder와 ContextCondenser에 post-compact tool snippet 복원, recent window 확대, tool result 보존 강화 로직을 추가해 장기 코드 실행 중 빌드/파일 근거 손실을 줄임
- MaxContextTokens=0 Auto 모드를 AppSettings, SettingsService 마이그레이션, 설정 UI, 오버레이 UI, 컨텍스트 사용량 표시, LLM 요청 본문에 연결하고 Auto 모드에서는 provider output cap 강제 주입을 제거
- 관련 회귀 테스트와 문서 README/DEVELOPMENT/CODE_CONTEXT_RELIABILITY_PLAN을 갱신하고 깨진 진단 문자열 기대값을 영어 기준으로 정리

검증:
- dotnet build src/AxCopilot/AxCopilot.csproj -c Release -v minimal -p:OutputPath=bin\\verify_context_reliability_followup\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_followup\\
- dotnet test src/AxCopilot.Tests/AxCopilot.Tests.csproj -c Release -v minimal --filter "AxAgentExecutionEngineTests|AgentQueryContextBuilderTests|ContextCondenserTests|SettingsServiceTests|AgentLoopDiagnosticsFormatterTests" -p:OutputPath=bin\\verify_context_reliability_followup_tests\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_followup_tests\\
- dotnet test src/AxCopilot.Tests/AxCopilot.Tests.csproj -c Release -v minimal --filter "AgentLoopQueryAssemblyServiceTests|AgentLoopPreLlmStageServiceTests|AgentLoopLlmRequestPreparationServiceTests|AgentMessageInvariantHelperTests|CodeTaskWorkingSetServiceTests|AgentLoopE2ETests" -p:OutputPath=bin\\verify_context_reliability_followup_tests2\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_followup_tests2\\
- dotnet build src/AxCopilot/AxCopilot.csproj -c Release -v minimal -p:OutputPath=bin\\verify_context_reliability_final\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_final\\

docs/DEVELOPMENT.md

@@ -1881,3 +1881,14 @@ UI ?遺우쁽????域뱀뮆???귐뗫솯?醫딆춦 ???袁る퓮 ?臾믩씜 ??疫
 - 테스트: `src/AxCopilot.Tests/Services/AgentLoopLlmDispatchStageServiceTests.cs`
 - 검증: `dotnet build src/AxCopilot/AxCopilot.csproj -c Release -v minimal -p:OutputPath=bin\\verify_llm_dispatch_stage_escalated2\\ -p:IntermediateOutputPath=obj\\verify_llm_dispatch_stage_escalated2\\` 경고 0 / 오류 0
 - 검증: `dotnet test src/AxCopilot.Tests/AxCopilot.Tests.csproj -c Release -v minimal --filter "AgentLoopLlmDispatchStageServiceTests|AgentLoopPreLlmStageServiceTests|AgentLoopQueryAssemblyServiceTests|AgentLoopIterationPreparationServiceTests|AgentLoopLlmRequestPreparationServiceTests|AgentMessageInvariantHelperTests|CodeTaskWorkingSetServiceTests|AgentLoopE2ETests" -p:OutputPath=bin\\verify_llm_dispatch_stage_tests_escalated2\\ -p:IntermediateOutputPath=obj\\verify_llm_dispatch_stage_tests_escalated2\\` 통과 43
+업데이트: 2026-04-16 07:40 (KST)
+- Code tab context reliability updates:
+  - `src/AxCopilot/Services/Agent/AxAgentExecutionEngine.cs` now deduplicates repeated system prompts, preserves full `ChatMessage` metadata during cloned turn preparation, and syncs structured tool transcript messages back into `conversation.Messages` so later turns keep durable tool history.
+  - `src/AxCopilot/Services/Agent/AgentQueryContextBuilder.cs` now restores recent compacted tool snippets into the post-compact context block, while `src/AxCopilot/Services/Agent/ContextCondenser.cs` increases the protected recent window and keeps more tool-result detail before truncation.
+  - `src/AxCopilot/Models/AppSettings.cs`, `src/AxCopilot/Services/SettingsService.cs`, `src/AxCopilot/ViewModels/SettingsViewModel.cs`, `src/AxCopilot/Views/SettingsWindow.xaml`, `src/AxCopilot/Views/SettingsWindow.xaml.cs`, `src/AxCopilot/Views/AgentSettingsWindow.xaml.cs`, `src/AxCopilot/Views/ChatWindow.xaml`, `src/AxCopilot/Views/ChatWindow.OverlaySettingsPresentation.cs`, and `src/AxCopilot/Views/ChatWindow.ContextUsagePresentation.cs` now support `MaxContextTokens = 0` as an Auto, model-aware context budget.
+  - `src/AxCopilot/Services/LlmService.cs` and `src/AxCopilot/Services/LlmService.ToolUse.cs` now omit output token caps for Auto budget mode instead of forcing the legacy 32K limit into provider payloads.
+  - `src/AxCopilot.Tests/Services/AxAgentExecutionEngineTests.cs`, `src/AxCopilot.Tests/Services/AgentQueryContextBuilderTests.cs`, `src/AxCopilot.Tests/Services/ContextCondenserTests.cs`, `src/AxCopilot.Tests/Services/SettingsServiceTests.cs`, and `src/AxCopilot.Tests/Services/AgentLoopDiagnosticsFormatterTests.cs` were updated with regression coverage for transcript sync, post-compact snippet recovery, Auto context budget migration, and prompt dedupe.
+- 검증:
+  - `dotnet build src/AxCopilot/AxCopilot.csproj -c Release -v minimal -p:OutputPath=bin\\verify_context_reliability_followup\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_followup\\` 경고 0 / 오류 0
+  - `dotnet test src/AxCopilot.Tests/AxCopilot.Tests.csproj -c Release -v minimal --filter "AxAgentExecutionEngineTests|AgentQueryContextBuilderTests|ContextCondenserTests|SettingsServiceTests|AgentLoopDiagnosticsFormatterTests" -p:OutputPath=bin\\verify_context_reliability_followup_tests\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_followup_tests\\` 통과 50
+  - `dotnet test src/AxCopilot.Tests/AxCopilot.Tests.csproj -c Release -v minimal --filter "AgentLoopQueryAssemblyServiceTests|AgentLoopPreLlmStageServiceTests|AgentLoopLlmRequestPreparationServiceTests|AgentMessageInvariantHelperTests|CodeTaskWorkingSetServiceTests|AgentLoopE2ETests" -p:OutputPath=bin\\verify_context_reliability_followup_tests2\\ -p:IntermediateOutputPath=obj\\verify_context_reliability_followup_tests2\\` 통과 38