Banks are supposed to take duration risk like this - they borrow short-term (deposits) to lend long-term (business loans and mortgages). The thing that's new in the current environment is that the fed has hiked rates so aggressively that even banks that took sane levels of duration risk are in danger of insolvency if their assets get marked to market.
You have that backwards. You borrow long term, then lend short term. Trying to keep enough liquidity to match withdrawal rates to "keep money working".
Lending long (10 year) on money deposited for only a year is a recipe for disaster.
Every other institution borrows long to lend short. That's how money is usually made in a financial company, like a hedge fund or something similar. Banks are the counterparty (in a cosmic sense) to that trade: they borrow short to lend long. It is an inherently unstable business model, but it works if you trust them enough.
