AttributeError on `with super()`

Bug report

Bug description:

Writing with super() raises an AttributeError. I ran into this implementing context managers inspired by contextlib.contextmnager but which had extra functionality. I can see no reason why with super() should be disallowed, and in fact, super().__enter__() and super().__exit__() work just fine.

Attempting to use an ExitStack as a work around was unsuccessful.

import sys
from contextlib import ExitStack

class Base:
    def __enter__(self):
        print("Entering base context manager")

    def __exit__(self, type, value, traceback):
        print("Exiting base context manager")

def __derived_enter__(self):
    self.context = self.contextlib_style_context()
    next(self.context)
    return self.context

def __derived_exit__(self, type, value, traceback):
    try:
        next(self.context)
    except StopIteration:
        pass

class DerivedUsingEnterExit(Base):
    def contextlib_style_context(self):
        print("Entering contextlib style context manager")
        super().__enter__()
        try:
            yield
        finally:
            super().__exit__(*sys.exc_info())

        print("Exiting contextlib style context manager")

    __enter__ = __derived_enter__
    __exit__ = __derived_exit__

class DerivedUsingWith(Base):
    def contextlib_style_context(self):
        print("Entering contextlib style context manager")
        with super():
            yield

        print("Exiting contextlib style context manager")

    __enter__ = __derived_enter__
    __exit__ = __derived_exit__

class DerivedUsingExitStack(Base):
    def contextlib_style_context(self):
        print("Entering contextlib style context manager")

        with ExitStack() as stack:
            stack.enter_context(super())
            yield

        print("Exiting contextlib style context manager")

    __enter__ = __derived_enter__
    __exit__ = __derived_exit__

# Runs successfully
with DerivedUsingEnterExit() as d:
    pass

# Raises AttributeError
with DerivedUsingWith() as d:
    pass

# Raises AttributeError
with DerivedUsingExitStack() as d:
    pass

CPython versions tested on:

3.13, 3.12

Operating systems tested on:

Windows

Start by reproducing the supplied DerivedUsingWith and DerivedUsingExitStack examples on CPython 3.13 or 3.12, then trace the super() and context-manager entry points involved. Compare them with the working super().enter() and super().exit() case; done means the intended behavior is decided and the reported AttributeError is covered by a regression test.