Generally, as you said, but if we as customers are still prioritized and if the supply runs out, they just take it back to their larger head office. There are also moments that create such conditions when many people need fiat in cash, for example during elections or other things, but personally I see that banks have anticipatory steps for important moments like this.
If you visit a bank center in each region, perhaps every service will be prioritized even though you request a withdrawal of all funds at the bank and the bank still has a lot of cash reserves for withdrawals from each customer, but the problem is that bank branches operating in the region have lower reserves and they manage the funds that we have saved for savings and loan programs that are profitable for them, we are only given the benefit of low interest. I have had the experience of withdrawing all funds from the bank and the bank responded that they had to wait several days because of the limited funds they had, in my opinion it is illogical that they have low reserves but we have kept all the fiat in savings.