[backport 2.3.x] TST (string dtype): fix invalid comparison error message and update test (pandas-dev#60176) (pandas-dev#60188)

(cherry picked from commit 9ec4a91)

Author: jorisvandenbossche

pandas/core/arrays/arrow/array.py

@@ -737,7 +737,7 @@ def _cmp_method(self, other, op):
                 try:
                     result[valid] = op(np_array[valid], other)
                 except TypeError:
-                    result = ops.invalid_comparison(np_array, other, op)
+                    result = ops.invalid_comparison(self, other, op)
                 result = pa.array(result, type=pa.bool_())
                 result = pc.if_else(valid, result, None)
         else:

pandas/tests/frame/test_arithmetic.py

@@ -13,7 +13,6 @@
 
 from pandas._config import using_string_dtype
 
-from pandas.compat import HAS_PYARROW
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -1563,17 +1562,19 @@ def test_comparisons(self, simple_frame, float_frame, func):
         with pytest.raises(ValueError, match=msg):
             func(simple_frame, simple_frame[:2])
 
-    @pytest.mark.xfail(
-        using_string_dtype() and HAS_PYARROW, reason="TODO(infer_string)"
-    )
     def test_strings_to_numbers_comparisons_raises(self, compare_operators_no_eq_ne):
         # GH 11565
         df = DataFrame(
             {x: {"x": "foo", "y": "bar", "z": "baz"} for x in ["a", "b", "c"]}
         )
 
         f = getattr(operator, compare_operators_no_eq_ne)
-        msg = "'[<>]=?' not supported between instances of 'str' and 'int'"
+        msg = "|".join(
+            [
+                "'[<>]=?' not supported between instances of 'str' and 'int'",
+                "Invalid comparison between dtype=str and int",
+            ]
+        )
         with pytest.raises(TypeError, match=msg):
             f(df, 0)