If a bank quietly added one cent to every customer’s account balance, what would happen?

The database records are not open for manipulation. The core banking software ensures that. Even if you were to somehow do this, the log and ledger alerts will flag such a transaction (and/or increase).

In order to increase money into each account, there has to be a ledger based income, which would then disburse the amount into other accounts, failing to do so, the audit will be seeing a bunch of flags.