Fix Type Annotations in pandas.core.dtypes

[gwrome]

Part of #25882

pandas.core.dtypes.dtypes and .missing have the following errors:

pandas/core/dtypes/dtypes.py:112: error: Need type annotation for 'shape'
pandas/core/dtypes/dtypes.py:117: error: Need type annotation for '_cache'
pandas/core/dtypes/dtypes.py:175: error: Definition of "type" in base class "PandasExtensionDtype" is incompatible with definition in base class "ExtensionDtype"
pandas/core/dtypes/dtypes.py:175: error: Definition of "kind" in base class "PandasExtensionDtype" is incompatible with definition in base class "ExtensionDtype"
pandas/core/dtypes/dtypes.py:220: error: Incompatible types in assignment (expression has type "Type[CategoricalDtypeType]", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:221: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:222: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:224: error: Incompatible types in assignment (expression has type "Tuple[str, str]", base class "_DtypeOpsMixin" defined the type as "Tuple[]")
pandas/core/dtypes/dtypes.py:225: error: Need type annotation for '_cache'
pandas/core/dtypes/dtypes.py:577: error: Definition of "type" in base class "PandasExtensionDtype" is incompatible with definition in base class "ExtensionDtype"
pandas/core/dtypes/dtypes.py:577: error: Definition of "kind" in base class "PandasExtensionDtype" is incompatible with definition in base class "ExtensionDtype"
pandas/core/dtypes/dtypes.py:588: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:589: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:593: error: Incompatible types in assignment (expression has type "Tuple[str, str]", base class "_DtypeOpsMixin" defined the type as "Tuple[]")
pandas/core/dtypes/dtypes.py:595: error: Need type annotation for '_cache'
pandas/core/dtypes/dtypes.py:732: error: Definition of "kind" in base class "ExtensionDtype" is incompatible with definition in base class "PandasExtensionDtype"
pandas/core/dtypes/dtypes.py:732: error: Definition of "type" in base class "ExtensionDtype" is incompatible with definition in base class "PandasExtensionDtype"
pandas/core/dtypes/dtypes.py:740: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:741: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:744: error: Incompatible types in assignment (expression has type "Tuple[str]", base class "_DtypeOpsMixin" defined the type as "Tuple[]")
pandas/core/dtypes/dtypes.py:746: error: Need type annotation for '_cache'
pandas/core/dtypes/dtypes.py:855: error: Definition of "type" in base class "PandasExtensionDtype" is incompatible with definition in base class "ExtensionDtype"
pandas/core/dtypes/dtypes.py:855: error: Definition of "kind" in base class "PandasExtensionDtype" is incompatible with definition in base class "ExtensionDtype"
pandas/core/dtypes/dtypes.py:864: error: Incompatible types in assignment (expression has type "str", base class "PandasExtensionDtype" defined the type as "None")
pandas/core/dtypes/dtypes.py:867: error: Incompatible types in assignment (expression has type "Tuple[str]", base class "_DtypeOpsMixin" defined the type as "Tuple[]")
pandas/core/dtypes/dtypes.py:869: error: Need type annotation for '_cache'

pandas/core/dtypes/missing.py:6: error: Module 'pandas._libs' has no attribute 'missing'

Working on a PR to fix these.