The issue is that Schwab (and all other brokerages) take your cash or money market balances and invest them in things like long-duration treasuries, mortgages, etc. and keep the interest. It's how they compensate themselves for all the free services they provide.
When interest rates rose and the resale value of those long-duration assets fell, Schwab found itself in the same position as banks. Deposit liabilities exceeded or came close to exceeding the value of the asset base. The exceptions are that (a) brokerage cash balances don't have guarantees like bank accounts do, which could make them more logical candidates for bank runs, and (b) it's not just withdraws that could break Schwab; a frenzy of asset buying or transfers by Schwab customers could force the brokerage to sell depreciated assets, recognize losses, and be unable to execute customers' orders. That's the doomsday scenario being priced in at Schwab.