Improve documentation for typing.get_type_hints (pythonGH-119928)

- Explicit list of what it does that is different from
  "just return __annotations__"
- Remove reference to PEP 563; adding the future import doesn't
  do anything to type aliases, and in general it will never make
  get_type_hints() less likely to fail.
- Remove example, as the Annotated docs already have a similar
  example, and it's unbalanced to have one example about this
  one edge case but not about other behaviors of the function.

(cherry picked from commit aa9fe98)

Co-authored-by: Jelle Zijlstra <[email protected]>
Co-authored-by: Alex Waygood <[email protected]>

Doc/library/typing.rst

@@ -2883,35 +2883,37 @@ Introspection helpers
    Return a dictionary containing type hints for a function, method, module
    or class object.
 
-   This is often the same as ``obj.__annotations__``. In addition,
-   forward references encoded as string literals are handled by evaluating
-   them in ``globals``, ``locals`` and (where applicable)
-   :ref:`type parameter <type-params>` namespaces.
-   For a class ``C``, return
-   a dictionary constructed by merging all the ``__annotations__`` along
-   ``C.__mro__`` in reverse order.
-
-   The function recursively replaces all ``Annotated[T, ...]`` with ``T``,
-   unless ``include_extras`` is set to ``True`` (see :class:`Annotated` for
-   more information). For example:
-
-   .. testcode::
-
-       class Student(NamedTuple):
-           name: Annotated[str, 'some marker']
-
-       assert get_type_hints(Student) == {'name': str}
-       assert get_type_hints(Student, include_extras=False) == {'name': str}
-       assert get_type_hints(Student, include_extras=True) == {
-           'name': Annotated[str, 'some marker']
-       }
+   This is often the same as ``obj.__annotations__``, but this function makes
+   the following changes to the annotations dictionary:
+
+   * Forward references encoded as string literals or :class:`ForwardRef`
+     objects are handled by evaluating them in *globalns*, *localns*, and
+     (where applicable) *obj*'s :ref:`type parameter <type-params>` namespace.
+     If *globalns* or *localns* is not given, appropriate namespace
+     dictionaries are inferred from *obj*.
+   * ``None`` is replaced with :class:`types.NoneType`.
+   * If :func:`@no_type_check <no_type_check>` has been applied to *obj*, an
+     empty dictionary is returned.
+   * If *obj* is a class ``C``, the function returns a dictionary that merges
+     annotations from ``C``'s base classes with those on ``C`` directly. This
+     is done by traversing ``C.__mro__`` and iteratively combining
+     ``__annotations__`` dictionaries. Annotations on classes appearing
+     earlier in the :term:`method resolution order` always take precedence over
+     annotations on classes appearing later in the method resolution order.
+   * The function recursively replaces all occurrences of ``Annotated[T, ...]``
+     with ``T``, unless *include_extras* is set to ``True`` (see
+     :class:`Annotated` for more information).
+
+   See also :func:`inspect.get_annotations`, a lower-level function that
+   returns annotations more directly.
 
    .. note::
 
-      :func:`get_type_hints` does not work with imported
-      :ref:`type aliases <type-aliases>` that include forward references.
-      Enabling postponed evaluation of annotations (:pep:`563`) may remove
-      the need for most forward references.
+      If any forward references in the annotations of *obj* are not resolvable
+      or are not valid Python code, this function will raise an exception
+      such as :exc:`NameError`. For example, this can happen with imported
+      :ref:`type aliases <type-aliases>` that include forward references,
+      or with names imported under :data:`if TYPE_CHECKING <TYPE_CHECKING>`.
 
    .. versionchanged:: 3.9
       Added ``include_extras`` parameter as part of :pep:`593`.