fix(openai): Claude Code 작업 경로 형식을 정규화한다

apps/edge/internal/openai/hot_path_light_test.go

@@ -330,6 +330,17 @@ func TestHotPathStageInputIsolation(t *testing.T) {
 	}
 }
 
+func TestCallerWorkingDirectoryFromClaudeCodeSystemPrompt(t *testing.T) {
+	task := "system: runtime context\n- Primary working directory: /workspace/claude-run\nuser: create index.html"
+	got, err := callerWorkingDirectory(task)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if want := "/workspace/claude-run"; got != want {
+		t.Fatalf("caller working directory = %q, want %q", got, want)
+	}
+}
+
 type scriptedLightPoolService struct {
 	providerFakeRunService
 	mu        sync.Mutex

apps/edge/internal/openai/hot_path_stage_input.go

@@ -178,7 +178,7 @@ func callerWorkingDirectory(task string) (string, error) {
 				break
 			}
 		}
-		for _, prefix := range []string{"Working directory:", "Current working directory:"} {
+		for _, prefix := range []string{"Working directory:", "Current working directory:", "- Primary working directory:"} {
 			if !strings.HasPrefix(line, prefix) {
 				continue
 			}