When a bank is lending you money it's creating the money they deposit in your account. This process is totally independent of people saving money in the bank.
The private bank is forced to search for a quantity of reserves proportional to the money it has created, but it does it a posteriori. The credit department only responsibility it's checking if loaning you money is a good business.
This is like saying that human exertion is independent of having to eat, because a person can go for a walk without first planning their next meal. This appears true on a small scale, but in the long run the inputs and outputs must balance.
For really big transactions, it becomes obvious. If I borrow $1 trillion from a bank, and immediately transfer it out, the bank can't get that money a posteriori. It can't transfer more than it has. It needs to borrow the entire sum, plus the reserve cushion, from someone else - other banks, depositors, or the Fed.
To be clear, I am in no way denying that bank lending increases the money supply. The contrast I'm drawing is with the Fed itself, which really can lend $1 trillion without getting it from anyone else.
If you move your loaned $1 trillion to another bank, your bank will have to find the reserves from other banks or from the Fed.
If it find it in other banks, no new reserves have been added, so, certainly, new money is in the system without the central bank doing nothing.
If it don't find the reserves in other banks at a good price, it will have to ask it to the Central Bank.
Now, the Central Bank have two options, it can give the reserves to the bank or it can refuse. If it refuse the private bank have to get the reserves in the inter-banks system. It have to. Otherwise it would be breaking the law.
So, it will be willing to pay anything necesary for the reserves. That will create additional demand in the reserves, and that mean that the interest rate will go up.
If the central bank wants to keep the interest rate in its target range it has to (it has not other option) to give the reserves to the bank.
Ergo, the central bank can choose the quantity of money in the system or the interest rate, but not both at the same time.
Modern central banks target the interest rate. Ergo, all this quantity of money thing is nonsense.
Your analogy breaks down because my eating and walking will not transfer energy to another human.
My own household experience with money and all analogies failed me when I first started thinking about these things. It only clicked once I started drawing up balance sheets.
As for the giant loan and transfer, I think that might be cleared soon-ish and only settled, with an interbank or fed loan if needed, at a later point in time after netting with other transfers.
The private bank is forced to search for a quantity of reserves proportional to the money it has created, but it does it a posteriori. The credit department only responsibility it's checking if loaning you money is a good business.