Sigh, you are confusing spread with real interest rates.
Spread = Interest on loans - Interest on deposits. The bigger the spread the more profitable the bank is.
Then review this formula: Nominal Interest Rates = Real Interest Rates + Expected Inflation.
Real interest rates is what the banks care about because that is how one increase value. Nominal interest rates is what the customer gets quoted and can’t go down below zero. Hold nominal interest rates fixed, decrease inflation (or increase deflation) and real rates increase. This is basically true because most banks have a positive leveraged duration (more long term loans then short term deposits)
One can argue that one can better manage (increase) the spread during times of inflation but the evidence is very mixed. But we do know that deflation does increase the spread, giving the bankers free money.