Pandas version checks

• I have checked that the issue still exists on the latest versions of the docs on main here

Location of the documentation

https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.astype.html

Documentation problem

Currently, the parameter specification

dtype: data type, or dict of column name

does not mention that Series are natively supported.

Suggested fix for documentation

Something along the lines of

dtype: string, data type, Series or Mapping of column name

Use a data type like object (string, numpy.dtype, pandas.ExtensionDtype or Python type) to cast entire pandas object to the same type. Alternatively, use a Mapping such as a dictionary of the form {col: dtype, …}, where col is a column label and dtype is the scalar type to cast one or more of the DataFrame’s columns to column-specific types.

One might also want to add: (#43837)

The Mapping is not allowed to contain column names that are present in the DataFrame.

I also noticed that the relevant code

essentially is a weaker version of isinstance(obj, collections.abc.Mapping) that I guess was introduced to also catch Series.
I would propose to think about replacing this with isinstance(obj, Mapping | Series) when appropriate.

Related: pandas-dev/pandas-stubs#410