In econ-101 it doesn't matter what the spread is, it isn't in itself rational to lend at 0%. That is taking on risk with no gain.
There must be some strange contortions in place to make this work. Whatever a "loan" is these days is going to be a totally regulatory construct with little connection to what they used to be way back when.
But they do not have to buy the same quantity of money as to what they are selling. When making a loan money is created out of thin air.
They do not have to hold deposits in the amount they lend out, but they do have to have the money. They have to hold back a fraction of the deposits.
If money was created out of thin air (in consumer banks), any loan with any interest rate (even negative one) would be highly profitable.
I am not talking about central banks.
What makes money for the bank is the difference of interest rate between money they buy and money they sell. Whether one or both are negative or positive doesn't really matter. Relative difference is what matters.