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.
I suspect it's both--and maybe even within the same billionaire sometimes (i.e. they diversify between methods).
One thing no rich person wants is to be killed or extorted (or the same for loved ones) based on their personal guarding of keys. People like that are already targets for more petty criminals after a million or two in ransom, so the last thing they would want is to gather the sort of expert criminal gangs you would if the prize was hundreds of millions. And also, people like this have a thousand things to think about on any given day, so the last thing they feel like dealing with would be physically securing their keys.
I suspect somebody like Musk would have a few million in keys on his person, but that's probably it.