fix: omit zero-fee private tx fee writes

[AztecBot]

Summary

Zero-fee private txs were still emitting a FeeJuice public-data write and forcing the private tx base rollup to prove membership of an existing fee-payer balance leaf. That made valid zero-fee private txs from fee payers without an initialized FeeJuice slot unprovable. This change treats the fee-payer write as absent when the computed transaction fee is zero.

Fix

• Emit zero private tx public-data writes when transaction_fee == 0.
• Skip the fee-payer public-data-tree update in that case, while keeping the existing membership update for positive fees.
• Add regressions for absent zero-balance fee leaves and the zero public-data-write blob encoding.

Testing

• ../../noir/noir-repo/target/debug/nargo test --package rollup_lib zero_fee_absent_fee_payer_balance_leaf_succeeds (failed before the fix with Membership check failed: public data leaf preimage does not exist in tree, passes after)
• ../../noir/noir-repo/target/debug/nargo test --package rollup_lib tx_base::tests::private_tx_base
• ../../noir/noir-repo/target/debug/nargo test --package rollup_lib zero_fee_omits_fee_payer_public_data_write
• git diff --check

Issues

• Closes AztecProtocol/aztec-claude#733 — zero-fee private txs require an existing FeeJuice public-data leaf.

---

Created by claudebox · group: kernels-audit-remediation