Move ContextManager and AsyncContextManager type hinting docs from typing to contextlib

[sterliakov]

Documentation

PEP585 deprecated typing.ContextManager and typing.AsyncContextManager in favour of their contextlib counterparts. However, contextlib documentation lacks any type hinting information and does not even list generic parameters.

Several relevant changes were discussed along #123523.

Currently there's no backlink from contextlib to typing docs, hence users don't have any trivial way to discover type parameters of ContextManager (that's worse than collections.abc.Generator where such a link exists).

Similarly to #123583, I propose to add a "Type hinting" section to both of them in contextlib documentation:

.. class:: AbstractContextManager

   An :term:`abstract base class` for classes that implement
   :meth:`object.__enter__` and :meth:`object.__exit__`. A default
   implementation for :meth:`object.__enter__` is provided which returns
   ``self`` while :meth:`object.__exit__` is an abstract method which by default
   returns ``None``. See also the definition of :ref:`typecontextmanager`.

   :class:`!AbstractContextManager` can be used in type annotations and accepts
   two type parameters: ``AbstractContextManager[T_co, ExitT_co]``. 
   The first type parameter, ``T_co``, represents the type returned by
   the :meth:`~object.__enter__` method. The optional second type parameter, 
   ``ExitT_co``, which defaults to ``bool | None``, represents the type 
   returned by the :meth:`~object.__exit__` method.

   .. versionadded:: 3.6

   .. versionchanged:: 3.13
      Added the optional second type parameter, ``ExitT_co``.