But in that sense, post-scarcity can't exist… so it can't be in that sense.
I suspect this is why "post-scarcity" is generally used to describe a state of affairs that does not currently exist, such as the idyllic Federation in Star Trek. In this context it was used to describe a society fundamentally different in significant ways from any past or present human one.
I don't know if I agree that post-scarcity cannot exist. I know that imagining a way to get there is very challenging. Knowing that scarcity is real certainly informs my politics, though.
In this context "scarcity" does not mean "There is not enough stuff", though that can be implied. It means there is a fundamentally limited amount of stuff and the aggregate demand is greater than the aggregate supply.
Given that the demand for resources is functionally infinite, I think this is basically accurate. Your objection to the existence of rich people is an objection to part of the aggregate demand, rather than to the description of resources as scarce.