BUG: Fix Series.str.contains with compiled regex on Arrow string dtype (#61942) and add whatsnew note

Author: Aniketsy

pandas/core/arrays/string_arrow.py

@@ -344,7 +344,7 @@ def _str_contains(
         na=lib.no_default,
         regex: bool = True,
     ):
-        if (isinstance(pat, re.Pattern) and regex) or flags:
+        if regex and (isinstance(pat, re.Pattern) or flags):
             return super()._str_contains(pat, case, flags, na, regex)
 
         return ArrowStringArrayMixin._str_contains(self, pat, case, flags, na, regex)

pandas/tests/strings/test_strings.py

@@ -10,7 +10,6 @@
 pytest.importorskip("pyarrow")
 
 from pandas import (
-    NA,
     DataFrame,
     Index,
     MultiIndex,
@@ -180,13 +179,14 @@ def test_empty_str_methods(any_string_dtype):
     tm.assert_series_equal(empty_str, empty.str.translate(table))
 
 
-def test_str_contains_compiled_regex_arrow():
-    # GH#61942
-    ser = Series(["foo", "bar", "baz", None], dtype="string[pyarrow]")
-    pat = re.compile(r"ba.")
+@pytest.mark.parametrize("dtype", ["string[pyarrow]"])
+def test_str_contains_compiled_regex_arrow_dtype(dtype):
+    ser = Series(["foo", "bar", "baz"], dtype=dtype)
+    pat = re.compile("ba.")
     result = ser.str.contains(pat)
-    expected = Series([False, True, True, NA], dtype="boolean[pyarrow]")
-    tm.assert_series_equal(result, expected)
+    assert str(result.dtype) == "bool[pyarrow]"
+    expected = Series([False, True, True], dtype="bool[pyarrow]")
+    tm.testing.assert_series_equal(result, expected)
 
 
 @pytest.mark.parametrize(