Add optional parameter for pd.factorize to handle new categories in categorical data dynamically
- [X] closes #12509 
- [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.
- [] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Issue with updating release notes (merge conflict):

Addition:
`- Enhanced :func:`pandas.factorize` to support an additional parameter `original_factorization`, allowing users to apply an existing factorization scheme to new data. This feature is useful for maintaining consistent category codes across different datasets (:issue:`12509`).`

Example usage:

```
original_data = ['a', 'b', 'c', 'c', 'd', 'e']
new_data = ['a', 'd', 'e', 'k']

# Original codes will be 0, 1, 2, 2, 3, 4
original_codes, original_uniques = pd.factorize(original_data)

new_codes, new_uniques = pd.factorize(new_data) # New codes will be 0, 1, 2, 3 given existing implementation
new_codes1, new_uniques1 = pd.factorize(new_data, original_factorization=(original_uniques, original_codes))

# New codes 1 will be 0, 3, 4, 5 to account for the mappings previously generated.
```


Thanks for the pull request, but it appears to have gone stale. Additionally the issue notes that this is a documentation change and a proposal to add a new argument needs a dedicated issue first before proceeding. Closing