Deposits are created jointly with each new loan on its balance (and destroyed when the loan pays back).
Offering higher deposits is actually a higher cost for a bank and lowers its profitability.
Deposits absolutely drive how much a bank can loan though. Otherwise banks wouldn’t bother taking deposits at all.
Look at the history of what the Narrow Bank attempted to do. It tried to drop the whole loan side of the business and effectively offer the fed funds rate directly to depositors. They were rejected because it was detrimental to the whole ecosystem of loans.