The vast majority of paper dollars deposited at a bank don’t physically stay in a bank in a vault. It is transferred into digital and held in the bank’s database. It is mostly digital. The “base” of the fiat system is US Treasury bonds, debt.
Cash is probably the closest thing to Bitcoin that exists in fiat, but it’s just pieces of paper that only cost a few cents to produce in paper and ink. Bitcoin costs a significant amount in energy and equipment to produce.