I see them as slightly different. Non-ergodicity means that the average of a sequence over time does not converge to the average of a huge number of parallel single gambles.
I see performativity as “creating the behaviour it describes”. Show someone a map of how to get from A to B, that act changes their choice. The act doesn’t just reflect reality, it creates it.
You could say that learning about ensemble means as the appropriate expectation value changes the investment choices of people. That would be true. And your observation that other who believe it too might fund you to continue the gamble is an example of performativity.
But in any case, the gamble is likely to fail!