What stopped the bank runs and failures was deposit insurance, not FDR’s bank holiday.
The Federal bank holiday lasted from March 6-13, 1933. On March 9, congress passed the Emergency Banking Act which, along with the Federal Reserve’s promise to provide liquidity to the banks, provided federal deposit insurance.
https://www.newyorkfed.org/medialibrary/media/research/epr/09v15n1/0907silb.pdf
Deposit insurance was formalized with the passage of the Banking Act in June 1933, which established the FDIC.
