ENH: Move factorizing for merge to EA interface
- [ ] closes #xxxx (Replace xxxx 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.


cc @jbrockmendel thoughts here? This would still need docs obviously
Generally looks good, mostly bikeshedding names a handful of nitpicks, otherwise im very happy to see this refactor 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. Sorry this fell off my radar, updated @MarcoGorelli is there a way to shut up the build about the missing example? There are a bunch of ea methods without examples... > is there a way to shut up the build about the missing example? There are a bunch of ea methods without examples...

+1.  Many of the examples are not particularly useful (I know because I wrote them to get the CI to shut up) yeah I'd expect pasting into 

https://github.com/pandas-dev/pandas/blob/13e034aaf68894079c61ace35e2f9d541fd64a1e/scripts/validate_docstrings.py#L44-L58

to work Looks like this has gone stale, so I'm bumping off the milestone Looks close to merge but has gone stale. Going to close to clear the queue but feel free to reopen when you have time to circle back