[Python] Remove the test usage of legacy dataset #20233

Currently the parquet tests cover both new and old dataset implementation. The usage of legacy dataset can be removed from the tests as the legacy ParquetDataset is being deprecated.

See #31529.

Reporter: Alenka Frim / @AlenkaF

Related issues:

• [Python] Deprecate the legacy ParquetDataset custom python-based implementation (requires)

PRs and other links:

• GitHub Pull Request #14031

_{Note: This issue was originally created as ARROW-16481. Please see the migration documentation for further details.}