Infer large_string type as pyarrow_numpy strings
- [ ] ref #54798 (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.

this covers the case where we don't overflow
Looks good to me. We should handle the case of a too large array that would need to be split for being able to cast to "string", but that's fine for a follow up. Can you open an issue for that? I was planning on keeping the other issue open