`.str.split` coerces `dtype` to `object`

**Describe the issue**:

The `.str.split` method coerces `dtype` from `string` to `object`. This behavior is also inconsistent with `pandas` (if that matters).

**Minimal complete verifiable example**:

Code
```python
import dask.dataframe as dd
import pandas as pd

data = {"c": ["a,b,c", "d,e,f", "g,h,i"]}

# `pandas`
df = pd.DataFrame(data, dtype="string[pyarrow]")
print(df.dtypes)
print(df["c"].str.split(",", n=1, expand=True).dtypes)

# `dask`
ddf = dd.from_pandas(df)
print(ddf.dtypes)
print(ddf["c"].str.split(",", n=1, expand=True).dtypes)
```

Output
```
c string[pyarrow]
dtype: object
0 string[pyarrow]
1 string[pyarrow]
dtype: object
c string[pyarrow]
dtype: object
0 object
1 object
dtype: object
```

**Environment**:

- Dask version: 2025.3.0
- Python version: 3.10.16
- Operating System: Ubuntu 24.04.2 LTS
- Install method (conda, pip, source): pip

Start by running the self-contained example in the issue and trace Dask DataFrame's `.str.split` implementation. Compare its output with pandas, then verify that splitting a `string[pyarrow]` column preserves that dtype in every expanded output column.

Written by the indexing model from the issue text.