BUG: DataFrame repr with ArrowDtype with extension
- [x] closes #54062 (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.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.


I _think_ it makes sense for the python `.type` of a pyarrow ExtensionType to be its storage's `.type`.

Might also close #54063? > Might also close #54063?

I'll leave that open for now. I interpreted that issue as maybe there's a fix that could be backported to 2.0.4 (but I am not sure that there is)