chore: add test for setgid bit inheritance in mkdir -p (#10412)

tests/by-util/test_mkdir.rs

@@ -908,6 +908,33 @@ fn test_mkdir_parent_mode_with_explicit_mode() {
     );
 }
 
+/// Test that nested directories inherit the setgid bit with mkdir -p.
+#[test]
+#[cfg(target_os = "linux")]
+fn test_mkdir_parent_inherits_setgid() {
+    let (at, mut ucmd) = at_and_ucmd!();
+
+    at.mkdir("parent");
+    at.set_mode("parent", 0o2755);
+
+    ucmd.arg("-p")
+        .arg("parent/child/grandchild")
+        .succeeds()
+        .no_stderr()
+        .no_stdout();
+
+    // All descendants should inherit the setgid bit (0o2000)
+    assert_eq!(at.metadata("parent").permissions().mode() & 0o2000, 0o2000);
+    assert_eq!(
+        at.metadata("parent/child").permissions().mode() & 0o2000,
+        0o2000
+    );
+    assert_eq!(
+        at.metadata("parent/child/grandchild").permissions().mode() & 0o2000,
+        0o2000
+    );
+}
+
 #[test]
 fn test_mkdir_concurrent_creation() {
     // Test concurrent mkdir -p operations: 10 iterations, 8 threads, 40 levels nesting