BUG: Assignment of pyarrow arrays yield unexpected dtypes
- [x] closes #56994 
- [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).
- [N.A.] 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/v3.0.0.rst` file if fixing a bug or adding a new feature.

During a column assignment in a `DataFrame`:
- If the column `value` is a pyarrow array (check tested with `lib.is_pyarrow_array`) `sanitize_array` sets `dtype` to `ArrowDtype(value.type)` 
- Else the standard `sanitize_array` processing are applied

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. > 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.

I'm still working on it. @jorisvandenbossche : Hello Joris, hope you're doing well would you have any news about [BUG: Assignment of pyarrow arrays yields unexpected dtypes](https://github.com/pandas-dev/pandas/issues/56994#top) ? Previously I was saying that "if a Series or a DataFrame is created or assigned with data dtype 'X' I would expect if it is possible, that it keeps the same 'X' dtype" but its only my humble opinion :-) and I would be equally happy to talk about it : maybe there is somewhere a discussion about how pyarrow types could be managed ? (thanks in advance !) Friendly ping @jorisvandenbossche  Hello @WillAyd: do you think this PR could be validated or should I have another approach ?  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.