DEPR: Series.argsort NA behavior
- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [x] [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.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Series.argsort has NA behavior different from EA.argsort/nargsort (xref #43840) that seems really useless to me.  This deprecates that behavior so in the future we can just pass through to the EA.

We _could_ expose the EA's na_position keyword, but let's wait on that until someone asks for it.  AFAIK this isn't really used.
```
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -295,7 +295,6 @@ Other API changes
 
 Deprecations
 ~~~~~~~~~~~~
-- Deprecated the behavior of :meth:`Series.argsort` in the presence of NA values; in a future version these will be sorted at the end instead of giving -1 (:issue:`54219`)
 - Deprecated 'broadcast_axis' keyword in :meth:`Series.align` and :meth:`DataFrame.align`, upcast before calling ``align`` with ``left = DataFrame({col: left for col in right.columns}, index=right.index)`` (:issue:`51856`)
 - Deprecated 'downcast' keyword in :meth:`Index.fillna` (:issue:`53956`)
 - Deprecated 'fill_method' and 'limit' keywords in :meth:`DataFrame.pct_change`, :meth:`Series.pct_change`, :meth:`DataFrameGroupBy.pct_change`, and :meth:`SeriesGroupBy.pct_change`, explicitly call ``ffill`` or ``bfill`` before calling ``pct_change`` instead (:issue:`53491`)
@@ -319,6 +318,7 @@ Deprecations
 - Deprecated the ``axis`` keyword in :meth:`DataFrame.ewm`, :meth:`Series.ewm`, :meth:`DataFrame.rolling`, :meth:`Series.rolling`, :meth:`DataFrame.expanding`, :meth:`Series.expanding` (:issue:`51778`)
 - Deprecated the ``axis`` keyword in :meth:`DataFrame.resample`, :meth:`Series.resample` (:issue:`51778`)
 - Deprecated the behavior of :func:`concat` with both ``len(keys) != len(objs)``, in a future version this will raise instead of truncating to the shorter of the two sequences (:issue:`43485`)
+- Deprecated the behavior of :meth:`Series.argsort` in the presence of NA values; in a future version these will be sorted at the end instead of giving -1 (:issue:`54219`)
``` updated+green Thanks @jbrockmendel 