ENH: Improve Type Annotations
Update typing on the following:
- `justify for DataFrame.to_string`
- - `justify for DataFrame.to_html`


- [ ] 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).
- [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.

cc @phofl @noatamir 
@Dr-Irv 
Thanks for the review. I have removed the changes for `nan_rep` and `tolerance` from this PR(will tackle those in another PR).
Also update type annotation for `justify` in `to_html` as per your suggestion.
Not sure what's the convention here, but if you want I can squash the commits into one or keep as is. 1. Can you rebase (merge with main)
2. Would you mind doing a similar PR in the pandas-stubs project?
 > Not sure what's the convention here, but if you want I can squash the commits into one or keep as is.

No need to squash - we do that when we merge > Can you rebase (merge with main)

Done
> Would you mind doing a similar PR in the pandas-stubs project?

I see the [to_html](https://github.com/pandas-dev/pandas-stubs/blob/6769e81bb95764fbc538c7aa95f5cc44c218704b/pandas-stubs/core/frame.pyi#L436) is already covered there. But can do for the [to_string()](https://github.com/pandas-dev/pandas-stubs/blob/6769e81bb95764fbc538c7aa95f5cc44c218704b/pandas-stubs/core/frame.pyi#L2180) 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.