The SVB was mark-to-market insolvent, not just undercapitalized. There's no indication that those marks were unrealistic; the market was orderly, and they were consistent with a naive NPV calculation, with a loss due to the increase in that discount rate. So it wasn't obvious that sufficient money to repay the depositors would exist even after zeroing the shareholders and creditors; if it were, then the SVB would probably have found a buyer.
Maybe enough depositors will leave money in the SVB at below-market interest rates that it will earn its way out of the hole. The FDIC has given depositors a special incentive to, since by guaranteeing all funds they've made the SVB the safest bank in the USA. If the depositors don't, then the FDIC will take the loss, and socialize it over all participating banks.
Per my other comment, the HTM accounting is a distraction. That accounting was compliant, but accounting doesn't define reality. The holders of long-term bonds take a real economic loss when interest rates increase, regardless of whether they sell. This may seem unintuitive since the cash flows don't change, but it couldn't be otherwise--if the bond is worth par, then why aren't any buyers willing to pay that?
