This is precisely why we have the FDIC -- if deposits are federally insured, there is much smaller incentive for depositors to withdraw their money out of fear of a bank run.
"As of December 31, 2022, the amount of estimated uninsured deposits in [SVB] U.S. offices that exceed the FDIC insurance limit was $151.5 billion. [from total deposits of $173,11B]." [0]