[Python] Error repeating df.to_parquet in pytest: "pyarrow.lib.ArrowKeyError: A type extension with name pandas.period already defined"

### Describe the bug, including details regarding any error messages, version, and platform.

Python version: 3.10.14
pyarrow version: 16.1.0
pandas version: 2.2.2
pytest version: 8.2.1

I have some apparently niche circumstances that trigger the following error:

```
/home/benf/repos/tetra/python/tests/test_minimal.py:24:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
/home/benf/micromamba/envs/tetra/lib/python3.10/site-packages/pandas/util/_decorators.py:333: in wrapper
return func(*args, **kwargs)
/home/benf/micromamba/envs/tetra/lib/python3.10/site-packages/pandas/core/frame.py:3113: in to_parquet
return to_parquet(
/home/benf/micromamba/envs/tetra/lib/python3.10/site-packages/pandas/io/parquet.py:476: in to_parquet
impl = get_engine(engine)
/home/benf/micromamba/envs/tetra/lib/python3.10/site-packages/pandas/io/parquet.py:63: in get_engine
return engine_class()
/home/benf/micromamba/envs/tetra/lib/python3.10/site-packages/pandas/io/parquet.py:169: in __init__
import pandas.core.arrays.arrow.extension_types # pyright: ignore[reportUnusedImport] # noqa: F401
/home/benf/micromamba/envs/tetra/lib/python3.10/site-packages/pandas/core/arrays/arrow/extension_types.py:59: in
pyarrow.register_extension_type(_period_type)
pyarrow/types.pxi:1954: in pyarrow.lib.register_extension_type
???
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

> ???
E pyarrow.lib.ArrowKeyError: A type extension with name pandas.period already defined

pyarrow/error.pxi:91: ArrowKeyError
========================================================= short test summary info =========================================================
FAILED python/tests/test_minimal.py::test_pyarrow_issue_2 - pyarrow.lib.ArrowKeyError: A type extension with name pandas.period already defined
```

It seems to have something to do with how pytest orchestrates its tests. Here is my minimal example:

test_minimal.py
```
import pytest
import pandas as pd

pytest_plugins = ["pytester"]

def test_pyarrow_issue(testdir, tmp_path):
path = str(tmp_path / "test.tar")
df = pd.DataFrame()
df.to_parquet(path)

def test_pyarrow_issue_2(testdir, tmp_path):
path = str(tmp_path / "test_2.tar")
df = pd.DataFrame()
df.to_parquet(path)
```

Running `pytest test_minimal.py` then triggers the error.

Notably, the error does *not* occur if either test is run independently, and it does not occur if the `testdir` fixture is removed or replaced with some other fixture. So I guess it has something to do with whatever `testdir` is doing under the hood. Presumably to do with how pandas/pyarrow get imported.

In my real case I would really quite like to keep using the `testdir` fixture, though I can probably find a different way to do things. But nonetheless this behaviour seemed worth reporting. Not sure if it is a pyarrow issue though, or whether it is more of a pytest issue, or maybe even pandas.

### Component(s)

Parquet, Python