Wide schema performance: eliminate quadratic column-count scaling

**Describe the bug**

Several independent code paths in the Parquet reader scale poorly with column count, leading to catastrophic performance on wide schemas. This epic-like issue tracks the general problem; individual PRs will reference it for context.

**To Reproduce**
N/A

**Expected behavior**

Parquet reader/writer operations and Arrow structures (RecordBatch, etc.) should scale linearly (ideally sub-linearly) with column count wherever practical.

**Additional context**

Start by mapping the independent Parquet reader and writer paths and the Arrow structures named in the issue, including RecordBatch. The issue provides no file names, tests, or reproduction; done means identifying and addressing the relevant quadratic column-count behavior so operations scale linearly or better where practical.

Written by the indexing model from the issue text.