DEPR: Enforce deprecation of na_sentinel
- [ ] 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
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] 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.

cc @jbrockmendel @jorisvandenbossche 
```
Error: /home/runner/work/pandas/pandas/pandas/core/base.py:1139:GL03:pandas.Series.factorize:Double line break found; please use only one blank line to separate sections or paragraphs, and do not leave blank lines at the end of docstrings
Error: /home/runner/work/pandas/pandas/pandas/core/algorithms.py:586:GL03:pandas.factorize:Double line break found; please use only one blank line to separate sections or paragraphs, and do not leave blank lines at the end of docstrings
Error: /home/runner/work/pandas/pandas/pandas/core/base.py:1139:GL03:pandas.Index.factorize:Double line break found; please use only one blank line to separate sections or paragraphs, and do not leave blank lines at the end of docstrings
``` @rhshadrach heads up - there's a merge conflict Thanks @mroeschke, it's now resolved. circleCI failure looks like its the float->dt64 astype issue, i.e. unrelated @rhshadrach looks like there's a merge conflict; otherwise, looks good to merge Thanks @rhshadrach 