DEPR: Positional arguments in Series.to_markdown

[rmhowe425]

• closes DEPR: Positional arguments in Series.to_markdown/string #57280
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

[rmhowe425]

@mroeschke Pinging on green

[twoertwein]

Looks good to me!

If you want to, you can also add overloads that already use the keyword-only syntax:

    @overload
    def to_markdown(
        self,
        buf: None = ...,
        *,
        mode: str = ...,
        index: bool = ...,
        storage_options: StorageOptions | None = ...,
        **kwargs,
    ) -> str: ...

    @overload
    def to_markdown(
        self,
        buf: IO[str],
        *,
        mode: str = ...,
        index: bool = ...,
        storage_options: StorageOptions | None = ...,
        **kwargs,
    ) -> None: ...

    @overload
    def to_markdown(
        self,
        buf: IO[str] | None,
        *,
        mode: str = ...,
        index: bool = ...,
        storage_options: StorageOptions | None = ...,
        **kwargs,
    ) -> str | None: ...

[twoertwein]

The changes look good to me, but the doc-test is failing (@mroeschke). The doc-test should definitely succeed before merging as the typing tests run after the doc-tests (in case mypy/pyright pick up something).

[twoertwein]

Thank you @rmhowe425 !