[Parent] Sparse Merkle forest: serialization, reconstruction, and commitment soundness

Tracking issue for the cluster of correctness, serialization, and commitment-soundness work on the sparse Merkle forest types (`PartialSmt`, `LargeSmt`/`LargeSmtForest`, `MmrPeaks`).

## Children

- #3470 — `PartialSmt` cannot be reconstructed from its `UniqueNodes` (round-trip bug with mixed inclusion/exclusion branches)
- #3527 — Investigate simplifying `PartialSmt` serialization via `UniqueNodes`
- #3510 — `pop_smts()` accepts duplicate roots, corrupting shared tree structure
- #3514 — Improve failure-case property test coverage for `LargeSmtForest`

## Related (filed under a more precise parent)

- #3512 — `MmrPeaks::hash_peaks` doesn't bind forest shape. Tracked under #3530 (the architecture follow-up for `0xMiden/security-issues#18`). Linked here for discoverability.

## Out of scope (perf, not correctness)

- #3511, #3507 — `LargeSmt` perf and storage optimizations.