diff --git a/pandas/core/arrays/string_arrow.py b/pandas/core/arrays/string_arrow.py
index 869cc34d5f61d..fd43ddfdf5432 100644
--- a/pandas/core/arrays/string_arrow.py
+++ b/pandas/core/arrays/string_arrow.py
@@ -697,9 +697,9 @@ def _reduce(
         self, name: str, *, skipna: bool = True, keepdims: bool = False, **kwargs
     ):
         if name in ["any", "all"]:
-            if not skipna and name == "all":
-                nas = pc.invert(pc.is_null(self._pa_array))
-                arr = pc.and_kleene(nas, pc.not_equal(self._pa_array, ""))
+            if not skipna:
+                nas = pc.is_null(self._pa_array)
+                arr = pc.or_kleene(nas, pc.not_equal(self._pa_array, ""))
             else:
                 arr = pc.not_equal(self._pa_array, "")
             return ArrowExtensionArray(arr)._reduce(
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 63e9e89cabd58..66799732be064 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -1062,25 +1062,62 @@ def test_any_all_datetimelike(self):
         assert df.any().all()
         assert not df.all().any()
 
-    def test_any_all_pyarrow_string(self):
+    def test_any_all_string_dtype(self, any_string_dtype):
         # GH#54591
-        pytest.importorskip("pyarrow")
-        ser = Series(["", "a"], dtype="string[pyarrow_numpy]")
+        if (
+            isinstance(any_string_dtype, pd.StringDtype)
+            and any_string_dtype.na_value is pd.NA
+        ):
+            # the nullable string dtype currently still raise an error
+            # https://github.com/pandas-dev/pandas/issues/51939
+            ser = Series(["a", "b"], dtype=any_string_dtype)
+            with pytest.raises(TypeError):
+                ser.any()
+            with pytest.raises(TypeError):
+                ser.all()
+            return
+
+        ser = Series(["", "a"], dtype=any_string_dtype)
         assert ser.any()
         assert not ser.all()
+        assert ser.any(skipna=False)
+        assert not ser.all(skipna=False)
 
-        ser = Series([None, "a"], dtype="string[pyarrow_numpy]")
+        ser = Series([np.nan, "a"], dtype=any_string_dtype)
         assert ser.any()
         assert ser.all()
-        assert not ser.all(skipna=False)
+        assert ser.any(skipna=False)
+        assert ser.all(skipna=False)  # NaN is considered truthy
 
-        ser = Series([None, ""], dtype="string[pyarrow_numpy]")
+        ser = Series([np.nan, ""], dtype=any_string_dtype)
         assert not ser.any()
         assert not ser.all()
+        assert ser.any(skipna=False)  # NaN is considered truthy
+        assert not ser.all(skipna=False)
 
-        ser = Series(["a", "b"], dtype="string[pyarrow_numpy]")
+        ser = Series(["a", "b"], dtype=any_string_dtype)
         assert ser.any()
         assert ser.all()
+        assert ser.any(skipna=False)
+        assert ser.all(skipna=False)
+
+        ser = Series([], dtype=any_string_dtype)
+        assert not ser.any()
+        assert ser.all()
+        assert not ser.any(skipna=False)
+        assert ser.all(skipna=False)
+
+        ser = Series([""], dtype=any_string_dtype)
+        assert not ser.any()
+        assert not ser.all()
+        assert not ser.any(skipna=False)
+        assert not ser.all(skipna=False)
+
+        ser = Series([np.nan], dtype=any_string_dtype)
+        assert not ser.any()
+        assert ser.all()
+        assert ser.any(skipna=False)  # NaN is considered truthy
+        assert ser.all(skipna=False)  # NaN is considered truthy
 
     def test_timedelta64_analytics(self):
         # index min/max