BUG: changing period array formats to specified date formats in `to_csv`
- This is intended to fix #51621
- This issue is that PeriodArrays can not change to the specified `date_format` in `to_csv`.
- The cause is that PeriodArray is established as `NDArrayBackedExtensionBlock` instead of `DatetimeLikeBlock` so that `df._mgr.to_native_types` does not change 'PeriodArray' to desired string format. This fix is added in after `df._mgr.to_native_types` to change `Period` to specified `date_format`.
- One unit test is added.

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. 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.