That was quite a weekend!
Some thoughts:
1. The government (FDIC/Fed/Treasury) won't let depositors at other banks lose their money after this. If they do, that would be like a perfect replay of Lehman. And they have the money ... or the money printer to be more precise.
2. But yes, depositors will probably move their deposits en masse this week regardless. As @changegonnacome pointed out, this shouldn't topple any bank immediately but some may be required to raise capital soon. The lending facility will give them the time to do so in an orderly manner if nothing else.
3. A mild recession could actually strengthen the balance sheets of many banks as interest rates will probably go down in that event and make treasuries and MBS more valuable. Of course a severe recession would be no good.
4. The FDIC limit will almost certainly be increased (and the FDIC will charge a higher price for it).
5. Speaking of which, I don't quite understand why private insurance companies do not sell deposit insurance...