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\\

src/AxCopilot.Tests/Services/AgentQueryContextBuilderTests.cs

@@ -96,4 +96,43 @@ public class AgentQueryContextBuilderTests
         result.ProtectedRecentNonSystemMessages.Should().BeGreaterThan(8);
         result.ToolResultAggregateBudgetChars.Should().BeGreaterThan(AgentToolResultBudget.DefaultAggregateBudgetChars);
     }
+
+    [Fact]
+    public void Build_ShouldRestoreRecentCompactedToolSnippetsIntoPostCompactContextMessage()
+    {
+        var sourceMessages = new List<ChatMessage>
+        {
+            new()
+            {
+                MsgId = "tool-call-1",
+                Role = "assistant",
+                Content = """{"_tool_use_blocks":[{"type":"tool_use","id":"call-restore","name":"file_read","input":{"path":"MainWindow.xaml"}}]}"""
+            },
+            new()
+            {
+                MsgId = "tool-result-1",
+                Role = "user",
+                Content = """{"type":"tool_result","tool_use_id":"call-restore","tool_name":"file_read","content":"<Window Title=\"Preview\" />"}"""
+            },
+            new()
+            {
+                MsgId = "boundary-1",
+                Role = "system",
+                MetaKind = "microcompact_boundary",
+                Content = "[previous conversation summary]"
+            },
+            new()
+            {
+                MsgId = "tail-1",
+                Role = "assistant",
+                Content = "recent tail"
+            }
+        };
+
+        var result = AgentQueryContextBuilder.Build(sourceMessages);
+        var postCompactMessage = result.Messages.Single(message => message.MetaKind == "post_compact_context");
+
+        postCompactMessage.Content.Should().Contain("recent compacted tool trace:");
+        postCompactMessage.Content.Should().Contain("file_read result:");
+    }
 }