Ah, but when they transfer that money, it'll be to some customer of some bank whose loan customers will also be transferring money in the other direction. This means, in practice, that the main constraint on a bank's ability to lend money is how willing all the other banks are to lend money at the time. The Bank of England paper linked earlier in the thread explains why this has undesirable economic implications that are missed by the incorrect money multiplier model.

The bank needs liquidity to settle inter-bank transfers after they've lent, some of that is deposits but they can also just borrow reserves from other banks if they need to do that.

The lending itself created new bank credit, it was never "funded". If the bank has capital adequacy, they make the loan.

When the deposit is transferred away essentially the target bank becomes the depositor in the source bank.

That's effectively what 'interbank lending' is. The central bank system then centralises that peer-to-peer processes.

Deposits are swapped for capital in the same way.