And while there may be objections to defining intelligence with respect to the Turing Test, I haven't heard of any definitions that are obviously and significantly better.

Our brains are stochastic parrots at least when it comes to communicating with text. People may digress into things like physical abilities, emotions, feelings, subjective experiences etc., but if we're talking about text, I'm not aware of a higher bar. In fact we probably don't know how to tell if an entity is "more intelligent" than the most intelligent humans because we won't be able to assess their intelligence.