Don't panic and rush to withdraw - that's definitely not the way to go. First, because your funds are locked in until the end of the term (you already figured that out), and second, because Binance and Bybit actually operate at a different level of reliability than FTX did. Yeah, there's a risk to keeping crypto on an exchange, but that's not the same as a guaranteed loss of money. The FTX situation was deliberate theft, not a technical crash or regulatory pressure.
The real problem in your situation isn't theft of your funds, but a lack of liquidity. If the exchange freezes accounts (even temporarily, due to audits, sanctions, or banking issues), you won't be able to withdraw your crypto while staking is active. That could be more painful than a complete collapse - you won't lose your money, but you won't be able to use it for months. Check the terms of this specific product: is there an early exit option with a penalty fee (usually 10-20% of the earnings, not the principal). If there is - that's insurance worth considering.
Practical advice: don't keep everything there. Even if you store the rest of your crypto in a cold wallet, having some funds on an active exchange for staking is fine, since you're not planning to touch it often anyway. The key is balance. If staking is eating up 80% of your portfolio while the other 20% sits in cold storage, that's skewed. The other way around would make more sense: most of it safe and secure, and only what you're prepared to leave untouched for a few months - and potentially lose in a worst-case scenario - in staking.