Re-integrate `pyarrow` `write_to_dataset` instead of `arrow._write_partitioned` in `dask`

**Describe the issue**:

Because of https://github.com/apache/arrow/issues/24440 (https://issues.apache.org/jira/browse/ARROW-8244), dask is using its own code to write a table to a partitioned pyarrow dataset. The code lives here:

https://github.com/dask/dask/blob/3124376d68bd3a15d381ce803ca066c7eef4c24f/dask/dataframe/io/parquet/arrow.py#L89-L101

Since this code was [added in March 2020](https://github.com/dask/dask/pull/6023), `pyarrow` came a long way. The original issue was [fixed in pyarrow in April 2020](https://github.com/apache/arrow/commit/ac3bfe47821cb8368f657860f115e88077eaf64d). There's a TODO in Dask code to re-integrate back `write_to_dataset`, we still need to do it. The custom code already required multiple bugfixes, and we can't be sure that it's up to date with `pyarrow`.

- Dask version: 2023.2.0+11.g0890b96b

cc @rjzamora .