If money moves electronically between bank accounts, how is physical cash “settled” or accounted for?

As Mark Harrison explained, when you settle or transfer electronically, there is no paper money involved.

However, if you deposit paper money into a bank account and then transfer the money electronically elsewhere, those are two different transactions. The paper money becomes part of the currency in circulation, and represents a portion on the ledger statement that each bank reports to the central bank (cash in hand), and the non-cash balance is the electronic equivalent of money.