BUG: groupby.apply drops the group key

[pyarchana]

Demo change touching pandas/core and a whatsnew file.

[precedent-bot]

From this project's review history

Nobody asked me. I read the files this pull request changes and found three conventions the project has settled before, each linked to where it was settled.

• Always include a whatsnew entry in the appropriate file for any bug fixes or new features.
  Established in #64119 and #61985.

  This helps keep the documentation up to date and informs users of changes.

• Use the code-block directive for demonstrating old behavior and the ipython directive for newly introduced behavior in the whatsnew files.
  Established in #63310 and #50626.

  This approach helps maintain clarity and accuracy in documenting changes across different versions of pandas.

• The first line of a docstring should be a single line summary.
  Established in #62880 and #36371.

  This helps maintain consistency and clarity in documentation across the project.

If this is wrong or out of date, a maintainer can say so: reply @precedent <the convention as it actually is> and I will hold the correction from then on.

[pyarchana]

@precedent whatsnew entries go in the file for the next release, not the current one

[pyarchana]

@precedent whatsnew entries go in the file for the next release, not the current one