BUG: read_csv with engine=pyarrow and numpy-nullable dtype
- [x] closes #56136 (Replace xxxx with the GitHub issue number)
- [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).
- [ ] 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.

Also makes this code path robust to always-distinguish behavior in #62040
> From the original issue, do you know where we are introducing float to lose precision when wanting the result type to be int?

In `arrow_table_to_pandas` the pyarrow[int64] columns get converted to np.float64, then in finalize_pandas_output that gets cast back to Int64.
 OK I see, it's `pyarrow.Table.to_pandas` casting the int to float when there's `null`.

What if in `arrow_table_to_pandas`, we always provide fallback `type_mapper={pyarrow ints : pandas nullable ints}` to avoid the lossy conversions, then afterwards we cast the pandas nullable ints to the appropriate type? That’s basically what this is currently doing, just not in that function since it is also called from other places.

I’m out of town for a few days. If you feel strongly that this logic should live inside that function I’ll move it when I get back Looking at this again, I'm skeptical of moving the logic into arrow_table_to_pandas.  The trouble is that between the table.to_pandas() and the .astype conversions, we have to do a bunch of other csv-keyword-specific stuff like set_index and column renaming.  (Just opened #62087 to clean that up a bit).  Shoe-horning all of that into arrow_table_to_pandas would make it a really big function in a way that i think is a net negative. Sorry in https://github.com/pandas-dev/pandas/pull/62053#issuecomment-3160877705, I meant for `arrow_table_to_pandas` to just have this change

```diff
diff --git a/pandas/io/_util.py b/pandas/io/_util.py
index 6827fbe9c9..2e15bd3749 100644
--- a/pandas/io/_util.py
+++ b/pandas/io/_util.py
@@ -85,7 +85,14 @@ def arrow_table_to_pandas(
         else:
             types_mapper = None
     elif dtype_backend is lib.no_default or dtype_backend == "numpy":
-        types_mapper = None
+        # Avoid lossy conversion to float64
+        # Caller is responsible for converting to numpy type if needed
+        types_mapper = {
+            pa.int8(): pd.Int8Dtype(),
+            pa.int16(): pd.Int16Dtype(),
+            pa.int32(): pd.Int32Dtype(),
+            pa.int64(): pd.Int64Dtype(),
+        }
     else:
         raise NotImplementedError
```

And then each IO parser is responsible for manipulating this result based on the IO arguments > And then each IO parser is responsible for manipulating this result based on the IO arguments

That would mean adding that logic to each of the 7 places where arrow_table_to_pandas is called, so we would almost-certainly be better off having it centralized.

If we get #62087 in then moving all the logic into arrow_table_to_pandas at least gets a little bit less bulky, so I can give it a try.
 This is plausibly nicer. Thanks @jbrockmendel 