REGR: Series[dt64/td64].astype(string)
- [x] closes #41409
- [ ] tests added / passed
- [ ] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [ ] whatsnew entry

This surfaces another bug in `StringArray.__getitem__` that I haven't looked into yet.
@meeseeksdev backport 1.3.x Something went wrong ... Please have  a look at my logs.