feat(batch): construct BatchNoteTree during batch construction

[mmagician]

Summary

First of two PRs for #3020. Wires the BatchNoteTree into batch construction on the Rust side, the foundation needed before the batch kernel can output (and later verify) BATCH_NOTE_TREE_ROOT in MASM.

The follow-up PR will wire these per-batch trees into block construction via BlockNoteTree::insert_batch_note_subtree and stop cross-batch note erasure.

Changes

• ProposedBatch::new_batch_inner builds a BatchNoteTree (via BatchNoteTree::with_contiguous_leaves) over the batch's final, post-erasure output notes. The tree is stored on ProposedBatch, exposed via a batch_note_tree() accessor, and included in into_parts. Serialization is unchanged since deserialization deterministically reconstructs the batch via new_batch_inner.
• ProvenBatch carries the tree's root in a new note_tree_root field, exposed via note_tree_root(), so the commitment flows to block construction and is ready for batch-kernel verification. LocalBatchProver passes the root from the ProposedBatch tree. This changes the ProvenBatch serialization format and the new_unchecked signature ([BREAKING]).
  • note_tree_root is stored as-is and is not recomputed/checked against output_notes by new_unchecked or deserialization; the doc comments warn it must not be trusted at a trust boundary until a consumer binds it. No current consumer trusts it (the block prover recomputes the tree from output notes).
• New error variant ProposedBatchError::BatchNoteTreeConstructionFailed (defensive; unreachable given the MAX_OUTPUT_NOTES_PER_BATCH bound equals the tree capacity).

Tests

• batch_note_tree_built_over_output_notes: tree root and leaf count match an independently built tree.
• batch_note_tree_excludes_erased_notes: notes erased within a batch are excluded from the tree.
• batch_note_tree_empty_when_no_output_notes: empty batch yields the empty-tree root; ProvenBatch::note_tree_root() matches.
• proven_batch_serialization_preserves_note_tree_root: round-trips a ProvenBatch and asserts the root survives.
• Extended proposed_batch_serialization to assert batch_note_tree equality after the round-trip.

Verified with cargo test -p miden-protocol -p miden-tx-batch-prover, the batch and block kernel test suites, and make lint.

[mmagician]

Suggested change

	/// The [`BatchNoteTree`] built over the batch's output notes, with note IDs packed at
	/// contiguous leaf indices in the same order as `output_notes`. Its root is the batch's
	/// note tree root.
	/// The [`BatchNoteTree`] built over the batch's output notes, with note IDs packed at
	/// contiguous leaf indices in the same order as `output_notes`.