BUG: Fix convert_dtypes for all na column and arrow backend

doc/source/whatsnew/v2.2.0.rst

@@ -281,7 +281,7 @@ Numeric
 
 Conversion
 ^^^^^^^^^^
--
+- Bug in :meth:`Series.convert_dtypes` not converting all NA column to ``null[pyarrow]`` (:issue:`55346`)
 -
 
 Strings

pandas/core/dtypes/cast.py

@@ -1133,7 +1133,16 @@ def convert_dtypes(
                 base_dtype = np.dtype(str)
             else:
                 base_dtype = inferred_dtype
-            pa_type = to_pyarrow_type(base_dtype)
+            if (
+                base_dtype.kind == "O"  # type: ignore[union-attr]
+                and len(input_array) > 0
+                and isna(input_array).all()
+            ):
+                import pyarrow as pa
+
+                pa_type = pa.null()
+            else:
+                pa_type = to_pyarrow_type(base_dtype)
             if pa_type is not None:
                 inferred_dtype = ArrowDtype(pa_type)
     elif dtype_backend == "numpy_nullable" and isinstance(inferred_dtype, ArrowDtype):

pandas/tests/series/methods/test_convert_dtypes.py

@@ -265,3 +265,11 @@ def test_convert_dtypes_pyarrow_to_np_nullable(self):
         result = ser.convert_dtypes(dtype_backend="numpy_nullable")
         expected = pd.Series(range(2), dtype="Int32")
         tm.assert_series_equal(result, expected)
+
+    def test_convert_dtypes_pyarrow_null(self):
+        # GH#55346
+        pa = pytest.importorskip("pyarrow")
+        ser = pd.Series([None, None])
+        result = ser.convert_dtypes(dtype_backend="pyarrow")
+        expected = pd.Series([None, None], dtype=pd.ArrowDtype(pa.null()))
+        tm.assert_series_equal(result, expected)