[EPIC] [Parquet] Variant improvements and optimizations (not gating stabilization)

**Is your feature request related to a problem or challenge? Please describe what you are trying to do.**

Companion to https://github.com/apache/arrow-rs/issues/10546, which tracks the work gating the `variant_experimental` flag switch. This epic collects Variant work that is worth doing but does not block stabilization: performance, ergonomics, and internal consolidation.

**Optimizations**
- [ ] https://github.com/apache/arrow-rs/pull/10358
- [ ] https://github.com/apache/arrow-rs/pull/9862 (cast perfectly shredded children directly, closed for now, to be revived once the cast alignment under https://github.com/apache/arrow-rs/issues/8982 lands)
- [ ] https://github.com/apache/arrow-rs/issues/8153 (achievable today by chaining `variant_get` + `shred_variant`, direct reshredding is an optimization)
- [ ] https://github.com/apache/arrow-rs/issues/8323
- [ ] https://github.com/apache/arrow-rs/issues/7960

**Ergonomics and internals**
- [ ] https://github.com/apache/arrow-rs/issues/9519 (achievable today with multiple `variant_get` calls + manual assembly)
- [ ] https://github.com/apache/arrow-rs/issues/9633
- [ ] https://github.com/apache/arrow-rs/issues/8605
- [ ] https://github.com/apache/arrow-rs/issues/8987

Start by reading the companion issue 10546 and the linked pull requests and issues listed under Optimizations and Ergonomics and internals. This is an epic rather than a single scoped change; done means selecting and completing one independently defined child item without blocking variant_experimental stabilization.

Written by the indexing model from the issue text.