Mypy reports issues with `to_string` on `Series` that seem erroneous

[mattinbits]

Describe the bug
When calling to_string on Series with index=False, mypy reports that this is not a valid variant, although it looks ok.

To Reproduce

Minimal example:

import pandas as pd

s = pd.Series(["A", "B", "C"])
print(s.to_string())
print(s.to_string(index=False))

mypy example.py

example.py:5: error: No overload variant of "to_string" of "Series" matches argument type "bool"  [call-overload]
example.py:5: note: Possible overload variants:
example.py:5: note:     def to_string(self, buf: Union[str, PathLike[str], WriteBuffer[str]], na_rep: str = ..., formatters: Any = ..., float_format: Any = ..., sparsify: Optional[bool] = ..., index_names: bool = ..., justify: Optional[str] = ..., max_rows: Optional[int] = ..., min_rows: Optional[int] = ..., max_cols: Optional[int] = ..., show_dimensions: bool = ..., decimal: str = ..., line_width: Optional[int] = ..., max_colwidth: Optional[int] = ..., encoding: Optional[str] = ...) -> None
example.py:5: note:     def to_string(self, buf: None = ..., na_rep: str = ..., formatters: Any = ..., float_format: Any = ..., sparsify: Optional[bool] = ..., index_names: bool = ..., justify: Optional[str] = ..., max_rows: Optional[int] = ..., min_rows: Optional[int] = ..., max_cols: Optional[int] = ..., show_dimensions: bool = ..., decimal: str = ..., line_width: Optional[int] = ..., max_colwidth: Optional[int] = ..., encoding: Optional[str] = ...) -> str

Please complete the following information:

• OS: Linux
• OS Version: Ubuntu 20.04
• python version: 3.9.14
• version of type checker: mypy 1.3.0
• version of installed pandas-stubs: 2.0.1.230501
• version of pandas: 2.0.1

Additional context
Nothing else to add

[Dr-Irv]

Looks like Series.to_string() is completely wrong as compared to the docs. Seems like at some point DataFrame.to_string() was copied over, but that was just plain wrong!

Need to correct the stubs and add some tests to test_series.py