`__future__` annotations breaks `TypedDict` `__required/optional_keys__`

Bug report

from __future__ import annotations appears to break TypedDict required/optional keys ending up in __required_keys__ and __optional_keys__. mypy works as expected though.

Using the example from https://peps.python.org/pep-0655/#usage-in-python-3-11 as the base

$ cat t.py
from __future__ import annotations

from typing_extensions import NotRequired, TypedDict

class Dog(TypedDict):
    name: str
    owner: NotRequired[str]

print("required", Dog.__required_keys__)
print("optional", Dog.__optional_keys__)
$ python3 t.py
required frozenset({'name', 'owner'})
optional frozenset()

With the __future__ import removed, works as expected:

$ cat t.py
from typing_extensions import NotRequired, TypedDict

class Dog(TypedDict):
    name: str
    owner: NotRequired[str]

print("required", Dog.__required_keys__)
print("optional", Dog.__optional_keys__)
$ python3 t.py
required frozenset({'name'})
optional frozenset({'owner'})

Note: breaks across different variations of total and Required/NotRequired and typing_extensions vs typing imports, above is just one example.

https://peps.python.org/pep-0655/#how-to-teach-this contains an example with the __future__ annotations import in place with no mention that it would not cause __required_keys__ and __optional_keys__ becoming populated as expected, so I'm assuming this is a bug.

Your environment

• CPython versions tested on:

  • 3.9.7 + NotRequired and TypedDict imports from typing_extensions
  • 3.10.7 + above mentioned imports from typing_extensions
  • current 3.11.0rc2+ + above mentioned imports from typing_extensions
  • current 3.11.0rc2+ above mentioned imports from typing

• Operating system and architecture: Linux x86_64

Start by running the t.py reproduction with and without from __future__ import annotations, across the listed Python versions and both typing and typing_extensions. Trace the TypedDict, Required, and NotRequired entry points to determine how postponed annotations affect key classification. Done means __required_keys__ and __optional_keys__ match the declared annotations for the reported variations.