It would be great if you could annotate a series, for example with -

def process_series(ser: pd.Series[int, str]) -> pd.Series[int, int]:

to indicate that the function should accept a string-valued series with an integer index, and output
int-valued series with an integer index.
It could be even better if you would build on that such that the series member's types could be inferred using TypeVars (for example, pd.Series[int,str].iloc would accept an integer and return a string), but that's not necessary - just a bonus or a later milestone.

To do that, you could add a new module (maybe "pandas.typing"?) that would contain these type-hints and would require minimal integration (if any) into the pandas' infrastructure. There's a similar package for "numpy" that's external to it called nptyping that could be used as a reference.