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GH-40270: [C++] Use LargeStringArray for casting when writing tables to CSV (#40271)



### Rationale for this change

Avoid casting failures when tables contains too long large string arrays.

### What changes are included in this PR?

Replace the usage of `StringArray` to `LargeStringArray`.

### Are these changes tested?

No extra test case is needed (as it is to fix some corner cases).

### Are there any user-facing changes?

No user-facing changes.

* GitHub Issue: #40270

Lead-authored-by: Tao He <sighingnow@gmail.com>
Co-authored-by: Antoine Pitrou <antoine@python.org>
Co-authored-by: Antoine Pitrou <pitrou@free.fr>
Signed-off-by: Antoine Pitrou <antoine@python.org>