TYP: Add overload for ser.rename_axis (#55412)

* Add overload for rename_axis

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

pandas/core/series.py

@@ -5004,8 +5004,44 @@ def reindex(  # type: ignore[override]
             tolerance=tolerance,
         )
 
+    @overload  # type: ignore[override]
+    def rename_axis(
+        self,
+        mapper: IndexLabel | lib.NoDefault = ...,
+        *,
+        index=...,
+        axis: Axis = ...,
+        copy: bool = ...,
+        inplace: Literal[True],
+    ) -> None:
+        ...
+
+    @overload
+    def rename_axis(
+        self,
+        mapper: IndexLabel | lib.NoDefault = ...,
+        *,
+        index=...,
+        axis: Axis = ...,
+        copy: bool = ...,
+        inplace: Literal[False] = ...,
+    ) -> Self:
+        ...
+
+    @overload
+    def rename_axis(
+        self,
+        mapper: IndexLabel | lib.NoDefault = ...,
+        *,
+        index=...,
+        axis: Axis = ...,
+        copy: bool = ...,
+        inplace: bool = ...,
+    ) -> Self | None:
+        ...
+
     @doc(NDFrame.rename_axis)
-    def rename_axis(  # type: ignore[override]
+    def rename_axis(
         self,
         mapper: IndexLabel | lib.NoDefault = lib.no_default,
         *,