diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index bdced4c496d14..0a851ae55fd68 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -746,6 +746,12 @@ def _reduce(
         axis: AxisInt | None = 0,
         **kwargs,
     ):
+        if self.dtype.na_value is np.nan and name in ["any", "all"]:
+            if name == "any":
+                return nanops.nanany(self._ndarray, skipna=skipna)
+            else:
+                return nanops.nanall(self._ndarray, skipna=skipna)
+
         if name in ["min", "max"]:
             result = getattr(self, name)(skipna=skipna, axis=axis)
             if keepdims:
@@ -754,6 +760,12 @@ def _reduce(
 
         raise TypeError(f"Cannot perform reduction '{name}' with string dtype")
 
+    def _wrap_reduction_result(self, axis: AxisInt | None, result) -> Any:
+        if self.dtype.na_value is np.nan and result is libmissing.NA:
+            # the masked_reductions use pd.NA -> convert to np.nan
+            return np.nan
+        return super()._wrap_reduction_result(axis, result)
+
     def min(self, axis=None, skipna: bool = True, **kwargs) -> Scalar:
         nv.validate_min((), kwargs)
         result = masked_reductions.min(
@@ -771,8 +783,11 @@ def max(self, axis=None, skipna: bool = True, **kwargs) -> Scalar:
     def value_counts(self, dropna: bool = True) -> Series:
         from pandas.core.algorithms import value_counts_internal as value_counts
 
-        result = value_counts(self._ndarray, sort=False, dropna=dropna).astype("Int64")
+        result = value_counts(self._ndarray, sort=False, dropna=dropna)
         result.index = result.index.astype(self.dtype)
+
+        if self.dtype.na_value is libmissing.NA:
+            result = result.astype("Int64")
         return result
 
     def memory_usage(self, deep: bool = False) -> int:
@@ -823,7 +838,13 @@ def _cmp_method(self, other, op):
             # logical
             result = np.zeros(len(self._ndarray), dtype="bool")
             result[valid] = op(self._ndarray[valid], other)
-            return BooleanArray(result, mask)
+            res_arr = BooleanArray(result, mask)
+            if self.dtype.na_value is np.nan:
+                if op == operator.ne:
+                    return res_arr.to_numpy(np.bool_, na_value=True)
+                else:
+                    return res_arr.to_numpy(np.bool_, na_value=False)
+            return res_arr
 
     _arith_method = _cmp_method
 
@@ -864,37 +885,6 @@ def _from_backing_data(self, arr: np.ndarray) -> StringArrayNumpySemantics:
         # we always preserve the dtype
         return NDArrayBacked._from_backing_data(self, arr)
 
-    def _reduce(
-        self, name: str, *, skipna: bool = True, keepdims: bool = False, **kwargs
-    ):
-        if name in ["any", "all"]:
-            if name == "any":
-                return nanops.nanany(self._ndarray, skipna=skipna)
-            else:
-                return nanops.nanall(self._ndarray, skipna=skipna)
-        else:
-            return super()._reduce(name, skipna=skipna, keepdims=keepdims, **kwargs)
-
-    def _wrap_reduction_result(self, axis: AxisInt | None, result) -> Any:
-        # the masked_reductions use pd.NA
-        if result is libmissing.NA:
-            return np.nan
-        return super()._wrap_reduction_result(axis, result)
-
-    def _cmp_method(self, other, op):
-        result = super()._cmp_method(other, op)
-        if op == operator.ne:
-            return result.to_numpy(np.bool_, na_value=True)
-        else:
-            return result.to_numpy(np.bool_, na_value=False)
-
-    def value_counts(self, dropna: bool = True) -> Series:
-        from pandas.core.algorithms import value_counts_internal as value_counts
-
-        result = value_counts(self._ndarray, sort=False, dropna=dropna)
-        result.index = result.index.astype(self.dtype)
-        return result
-
     # ------------------------------------------------------------------------
     # String methods interface
     _str_na_value = np.nan