`types._GeneratorWrapper` is no longer consistent with `types.GeneratorType`/`types.CoroutineType`

Bug report

Bug description:

types.coroutine() uses _GeneratorWrapper as a wrapper for generator iterators in cases where the callable object is not a user-defined function (but is, for example, a generator function compiled via Cython/Nuitka). However, the implementation has not been updated for 11 years and therefore does not provide certain properties, such as:

• GeneratorType.gi_suspended (Python ≥3.11, python/cpython#30633)
• CoroutineType.cr_suspended (Python ≥3.11, python/cpython#30633)
• CoroutineType.cr_origin (Python ≥3.7, python/cpython#5250)

As a result, the objects returned by the new function do not look exactly like types.GeneratorType/types.CoroutineType, which in particular makes them incompatible with the inspect.getgeneratorstate() and inspect.getcoroutinestate() functions:

>>> from inspect import getcoroutinestate, getgeneratorstate
>>> from types import coroutine
>>> def generator_function():
...     return
...     yield  # generator definition
>>> @coroutine
... def coroutine_function():
...     return generator_function()
>>> gencoro = coroutine_function()
>>> getgeneratorstate(gencoro)
Traceback (most recent call last):
AttributeError: '_GeneratorWrapper' object has no attribute 'gi_suspended'
>>> getcoroutinestate(gencoro)
Traceback (most recent call last):
AttributeError: '_GeneratorWrapper' object has no attribute 'cr_suspended'

Interestingly, there was already an attempt to add *_suspended in #133373 (see https://github.com/python/cpython/issues/133372#issuecomment-2849166854), but the PR was closed in favor of removing the TODO comment, and this side issue was apparently overlooked.

Related: cython/cython#7448.

CPython versions tested on:

3.11, 3.12, 3.13, 3.14

Operating systems tested on:

Linux

Linked PRs

• gh-143609

Start with Lib/types.py lines 255-289, then inspect.getgeneratorstate() and inspect.getcoroutinestate(), which the report identifies as affected entry points. Compare the wrapper's exposed attributes with GeneratorType and CoroutineType; done means both inspect functions work for the wrapped objects and the listed suspension and origin properties are consistent.