update pd.DataFrame.merge - add typing for `how` parameter
- [x] closes #48503
- [ ] [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.

PR for `pandas-stubs`: https://github.com/pandas-dev/pandas-stubs/pull/289 > Thx, can you add this for join too? Additionally, I think we are typing how internally too, would be great to add this there too

For `DataFrame.join`, you probably need `MergeHow | Literal["cross"]`.

Could also use `MergeHow` in `Index.join/_join* `(in pandas/core/indexes/base.py) and for the align methods `NDFrame/DataFrame/Series.align` (in pandas/core/{generic,frame,series}.py) MergeHow includes cross already? > MergeHow includes cross already?

You are right :) Forget about my comment :) 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.