diff --git a/tests/main/test_public_api_signature_baseline.py b/tests/main/test_public_api_signature_baseline.py
index 90327169c..00b4d07ea 100644
--- a/tests/main/test_public_api_signature_baseline.py
+++ b/tests/main/test_public_api_signature_baseline.py
@@ -344,21 +344,64 @@ def _type_to_str(tp: Any) -> str:
 
 
 def _normalize_union_str(type_str: str) -> str:
-    """Normalize a union type string by sorting its components."""
+    """Normalize a union type string by sorting its components recursively."""
     try:
         tree = ast.parse(type_str, mode="eval")
     except SyntaxError:  # pragma: no cover
         return type_str
-    if not isinstance(tree.body, ast.BinOp) or not isinstance(tree.body.op, ast.BitOr):
-        return type_str
 
-    def collect_union_parts(node: ast.expr) -> list[str]:
+    def normalize_node(node: ast.expr) -> str:
         if isinstance(node, ast.BinOp) and isinstance(node.op, ast.BitOr):
-            return collect_union_parts(node.left) + collect_union_parts(node.right)
-        return [ast.unparse(node)]
 
-    parts = collect_union_parts(tree.body)
-    return " | ".join(sorted(parts))
+            def collect_union_parts(n: ast.expr) -> list[str]:
+                if isinstance(n, ast.BinOp) and isinstance(n.op, ast.BitOr):
+                    return collect_union_parts(n.left) + collect_union_parts(n.right)
+                return [normalize_node(n)]
+
+            parts = collect_union_parts(node)
+            return " | ".join(sorted(parts))
+        if isinstance(node, ast.Subscript):
+            value = ast.unparse(node.value)
+            if isinstance(node.slice, ast.Tuple):
+                args = [normalize_node(elt) for elt in node.slice.elts]
+                return f"{value}[{', '.join(args)}]"
+            return f"{value}[{normalize_node(node.slice)}]"
+        return ast.unparse(node)
+
+    return normalize_node(tree.body)
+
+
+@pytest.mark.parametrize(
+    ("input_str", "expected"),
+    [
+        ("str | int", "int | str"),
+        ("str | int | None", "None | int | str"),
+        ("int", "int"),
+        ("Mapping[str, str]", "Mapping[str, str]"),
+        ("Mapping[str, str | list[str]]", "Mapping[str, list[str] | str]"),
+        ("Mapping[str, list[str] | str]", "Mapping[str, list[str] | str]"),
+        ("Mapping[str, str | list[str]] | None", "Mapping[str, list[str] | str] | None"),
+        ("dict[str, int | str | None]", "dict[str, None | int | str]"),
+        ("list[str | int]", "list[int | str]"),
+        ("tuple[str | int, bool | None]", "tuple[int | str, None | bool]"),
+    ],
+)
+def test_normalize_union_str(input_str: str, expected: str) -> None:
+    """Test _normalize_union_str correctly normalizes union types recursively."""
+    assert _normalize_union_str(input_str) == expected
+
+
+@pytest.mark.parametrize(
+    ("type_a", "type_b"),
+    [
+        ("Mapping[str, str | list[str]]", "Mapping[str, list[str] | str]"),
+        ("str | int | None", "None | str | int"),
+        ("dict[str, int | str]", "dict[str, str | int]"),
+    ],
+)
+def test_normalize_union_str_equivalence(type_a: str, type_b: str) -> None:
+    """Test that different orderings of the same union type normalize to the same string."""
+    assert _normalize_union_str(type_a) == _normalize_union_str(type_b)
 
 
 def _normalize_type(tp: Any) -> str:  # noqa: PLR0911