[Python] Remove the legacy ParquetDataset custom python-based implementation #31303

We might want to keep the actual ParquetDataset class (ARROW-9720), but we should still remove the custom / legacy implementation (which is using the deprecated filesystem interface, so this is also blocking ARROW-15761)

Reporter: Joris Van den Bossche / @jorisvandenbossche

Related issues:

• [Python] Remove the deprecated pyarrow.filesystem legacy implementations (blocks)
• [Python] Deprecate the legacy ParquetDataset custom python-based implementation (is blocked by)
• [Python] Long-term fate of pyarrow.parquet.ParquetDataset (is related to)

_{Note: This issue was originally created as ARROW-15868. Please see the migration documentation for further details.}