"Uninsured" doesn't mean "all of your money is gone, sucks to be you", it means "you'll take a haircut proportional to the amount of missing assets from the pool." And yes, if the bank is a Ponzi scheme, then that pool is empty, but SVB's problem is liquidity, not overall solvency. The money is there, it's just locked at a suboptimal interest rate, which may cost you 10 - 20%.
This isn't like FTX where your "assets" are worthless IOUs written to yourself.
May also be solvency - their assets are MBSes whose market value went down with the interest rate rise, that being the proximate cause of the panic that set off the bank run.
No. If I crash my car into a $80,000 BMW and totaling it—and I have no insurance—the other party will still be able to sue me and partially recover their losses. Maybe they get $63k from me and eat the other $17k.
The bank has assets. Just not enough to cover all liabilities. That's why you see the term "haircut" being used a lot in these threads.
This isn't like FTX where your "assets" are worthless IOUs written to yourself.