First, Schwab has over $350 billion in deposits. That has declined from over $450 billion at it's peak last year. Unlike the regional banks, I'm guessing that this is less due to capital flight (moving from Schwab to another bank), and more due to customers moving their assets from cash (Schwab pays a pitiful 0.5%), and into higher-yielding assets (like treasuries or money market funds). The assets stay on Schwab, but it still decreases Schwab's deposits and liquidity.
Moreover, I was stunned when I saw that Schwab reported over $150 billion in held-to-maturity assets of over 5 year duration (and over $100 billion of that is in bonds of greater than 10 year duration). Again, not a banking analyst (also not sure if some of this is hedged), but this looks very aggressive to me, and could result in a significant $15+ billion loss that significantly impairs tangible book value. Regulators really dropped the ball by not incorporating more stress scenarios based on interest rates.
Schwab recently sent a notice that they have a large amount of liquidity, and it is unlikely that they'll need to sell the HTM maturities. Still, there is a concern that Schwab customers will panic and put that to the test. The falling stock price and posts like this will probably raise awareness of Schwab's issues.
Personally, I'm pretty disappointed in Schwab, but my opinion is that your brokerage assets are almost certainly safe. Schwab still has a decent cushion (including equity, preferred, and debt), and operates a pretty valuable franchise. Equity holders could be in trouble due to concerns over negative carry though (their long-term HTM assets could yield less than the cost to attract new deposits).
Personally, I turned off the margin at Schwab this weekend out of an abundance of caution, to reduce the likelihood that I'll be an unsecured creditor if shit truly hits the fan. However, that will almost certainly not be necessary.