diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index 083acf16ec758..c9abef226770c 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -90,8 +90,11 @@ class StringDtype(StorageExtensionDtype):
 
     name = "string"
 
-    #: StringDtype.na_value uses pandas.NA
-    na_value = libmissing.NA
+    #: StringDtype().na_value uses pandas.NA
+    @property
+    def na_value(self) -> libmissing.NAType:
+        return libmissing.NA
+
     _metadata = ("storage",)
 
     def __init__(self, storage=None) -> None:
@@ -335,13 +338,11 @@ def _from_sequence(cls, scalars, *, dtype: Dtype | None = None, copy=False):
             na_values = scalars._mask
             result = scalars._data
             result = lib.ensure_string_array(result, copy=copy, convert_na_value=False)
-            result[na_values] = StringDtype.na_value
+            result[na_values] = libmissing.NA
 
         else:
-            # convert non-na-likes to str, and nan-likes to StringDtype.na_value
-            result = lib.ensure_string_array(
-                scalars, na_value=StringDtype.na_value, copy=copy
-            )
+            # convert non-na-likes to str, and nan-likes to StringDtype().na_value
+            result = lib.ensure_string_array(scalars, na_value=libmissing.NA, copy=copy)
 
         # Manually creating new array avoids the validation step in the __init__, so is
         # faster. Refactor need for validation?
@@ -396,7 +397,7 @@ def __setitem__(self, key, value):
         # validate new items
         if scalar_value:
             if isna(value):
-                value = StringDtype.na_value
+                value = libmissing.NA
             elif not isinstance(value, str):
                 raise ValueError(
                     f"Cannot set non-string value '{value}' into a StringArray."
@@ -497,7 +498,7 @@ def _cmp_method(self, other, op):
 
         if op.__name__ in ops.ARITHMETIC_BINOPS:
             result = np.empty_like(self._ndarray, dtype="object")
-            result[mask] = StringDtype.na_value
+            result[mask] = libmissing.NA
             result[valid] = op(self._ndarray[valid], other)
             return StringArray(result)
         else:
@@ -512,7 +513,7 @@ def _cmp_method(self, other, op):
     # String methods interface
     # error: Incompatible types in assignment (expression has type "NAType",
     # base class "PandasArray" defined the type as "float")
-    _str_na_value = StringDtype.na_value  # type: ignore[assignment]
+    _str_na_value = libmissing.NA  # type: ignore[assignment]
 
     def _str_map(
         self, f, na_value=None, dtype: Dtype | None = None, convert: bool = True
diff --git a/pandas/core/arrays/string_arrow.py b/pandas/core/arrays/string_arrow.py
index 3e3df5a3200c1..bb2fefabd6ae5 100644
--- a/pandas/core/arrays/string_arrow.py
+++ b/pandas/core/arrays/string_arrow.py
@@ -242,8 +242,9 @@ def astype(self, dtype, copy: bool = True):
     # ------------------------------------------------------------------------
     # String methods interface
 
-    # error: Cannot determine type of 'na_value'
-    _str_na_value = StringDtype.na_value  # type: ignore[has-type]
+    # error: Incompatible types in assignment (expression has type "NAType",
+    # base class "ObjectStringArrayMixin" defined the type as "float")
+    _str_na_value = libmissing.NA  # type: ignore[assignment]
 
     def _str_map(
         self, f, na_value=None, dtype: Dtype | None = None, convert: bool = True
diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 9683c1dd93645..99b2082d409a9 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -676,11 +676,14 @@ class DatetimeTZDtype(PandasExtensionDtype):
     kind: str_type = "M"
     num = 101
     base = np.dtype("M8[ns]")  # TODO: depend on reso?
-    na_value = NaT
     _metadata = ("unit", "tz")
     _match = re.compile(r"(datetime64|M8)\[(?P<unit>.+), (?P<tz>.+)\]")
     _cache_dtypes: dict[str_type, PandasExtensionDtype] = {}
 
+    @property
+    def na_value(self) -> NaTType:
+        return NaT
+
     @cache_readonly
     def str(self):
         return f"|M8[{self._unit}]"
@@ -1450,7 +1453,9 @@ class BaseMaskedDtype(ExtensionDtype):
     base = None
     type: type
 
-    na_value = libmissing.NA
+    @property
+    def na_value(self) -> libmissing.NAType:
+        return libmissing.NA
 
     @cache_readonly
     def numpy_dtype(self) -> np.dtype:
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index 56fcec751749b..5731d476cef10 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -409,7 +409,10 @@ class Float64Index(NumericIndex):
     __doc__ = _num_index_shared_docs["class_descr"] % _index_descr_args
 
     _typ = "float64index"
-    _engine_type = libindex.Float64Engine
     _default_dtype = np.dtype(np.float64)
     _dtype_validation_metadata = (is_float_dtype, "float")
     _is_backward_compat_public_numeric_index: bool = False
+
+    @property
+    def _engine_type(self) -> type[libindex.Float64Engine]:
+        return libindex.Float64Engine