[TST] Parse arrow_dtype as datetime index
- [X] closes #57930(Replace with the GitHub issue number)
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

As feedback : 
- On my pandas version (not main as I don't have a C compiler), the returned dataframes have the following dtypes : 
   - index : datetime64[ns]
   - int64[pyarrow]
I would have expected the index to also be a pyarrow dtype, but unsure if I need to enforce that. I checked some of the fails : 
- The new test fails even if was stated to be working on main https://github.com/pandas-dev/pandas/issues/57930#issuecomment-2248564090. Strange.
- There is an error on ISORT error, but Ruff corrects it differently 🙄 


 This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Keep it open please 🫣 Thanks for the pull request, but it appears to have gone stale. If interested in continuing, please merge in the main branch, address any review comments and/or failing tests, and we can reopen. @mroeschke : I have done all you requested. 