When you buy any stock through a normal major broker in the US, you are covered by SIPC, which covers up to $500k. However, that is covering your stock certificate, not the thing backing it. In other words, if you invest in some stock and it goes bankrupt, then you aren't covered. It's only covered if the broker somehow loses your actual position.
Yes, we're referring to the same idea. I'm not sure a billionaire would use a broker, since they could buy stocks directly to avoid the risk of broker failure. However, if they wanted to invest in Bitcoin, it might be more practical for them to use an ETF instead of managing their own private keys.
That said, a very wealthy individual likely owns a significant amount of real estate. If they chose to self-custody their Bitcoin, they could set up a secure multi-sig, ensuring protection without relying on the state.