You're right that FDIC doesn't have to, but it's in everyone's interest that people keep keeping their money in a bank, so the long and the short of it is that the FDIC's playbook is to find another bank to buy SVB (for pennies on the dollar), and as part of that deal the purchaser bank will make them whole. FDIC doesn't necessarily have to do that, but it's what they've done in the past, so guessing that they will do something similar this time around isn't out of the question.
For your explained meaning, it is in depositor's individual interest to remove their money. Get cash or t-bills. Also get a credit union account where they work for the members.
