REF: extract params used in Series.__repr__
This PR gives flexibility if we want the series string output to be like the Series repr, but with some adjustments.

So with this PR we we can now do:

```python
>>> params = pd.io.formats.format.get_series_repr_params(ser)
>>> params[my_param] = new_value
>>> ser.to_string(**params)
```

Followup to #43987.

thanks @topper-123 