Probe target
  repo: /code/cardano-api
  git HEAD: b951a6380b8896a199fd2c4b751600b16029233b
  tag/package version: cardano-api-10.19.1.0
  source: cardano-api/src/Cardano/Api/Tx/Internal/Fee.hs:1028-1051

Inspected signature
  makeTransactionBodyAutoBalance
    :: ShelleyBasedEra era
    -> SystemStart
    -> LedgerEpochInfo
    -> LedgerProtocolParameters era
    -> Set PoolId
    -> Map StakeCredential Coin
    -> Map DRepCredential Coin
    -> UTxO era
    -> TxBodyContent BuildTx era
    -> AddressInEra era
    -> Maybe Word
    -> Either (TxBodyErrorAutoBalance era) (BalancedTxBody era)

The implementation comment states that it evaluates scripts, computes minimum
fees, updates the fee, then balances and creates change. Its input is a fixed
TxBodyContent and its result is returned only after auto-balancing; the type has
no callback receiving the candidate transaction.

Conclusion
  Ordinary fee/change balancing is supported. A caller can express fee-dependent
  outputs or a final-output-dependent redeemer by inspecting BalancedTxBody,
  constructing a fresh TxBodyContent, and calling again in a bounded outer loop.
  There is no in-call final-transaction observation/re-entry hook.