I can see how automation would make poor and middle income people poorer, but I don’t see why automation would depress the wealth of the already wealthy.

Well, "people" here means 99% or 99.9% or maybe a couple extra nines. I really didn't mean the next 0.01%.

Anyway, it can, by a complex process that makes an entire society poorer once people gets thrown out of the economy. That includes the absurdly rich too. It's just that if this is the only point where it bothers you, honestly I don't even care about your opinion.

Automation can put everyone out of a job, for all I care about jobs and the economy. They are potentially mutually beneficial, but usually extremely unfavorable to labor in terms of sharing profits. No jobs means no unemployment.