On the other side: Parrots cannot recognize themselves in a mirror https://talkieparrot.com/behavior/can-parrots-recognize-them..., while monkeys can https://en.wikipedia.org/wiki/Mirror_test . I consider the mirror test a better test for a higher form of intelligence than simply being able to simulate talking. So the real question nowadays would be: Can GPT-4 pass the mirror test? Can it detect it‘s own output, if you echo it back to it?
The problem is also that intelligence isn't on some kind of a line where a specific test tells you that you're closer to a base amount of intelligence needed for sentience. It's a whole bunch of things combined in some yet to be defined way that ends up allowing for the development of intelligence.
As for GPT-4 - it can't even recognize for itself whether data is good or bad, and it can't even recognize that it doesn't know something; IMO right now it's still basically just a black box that takes an input and produces a statistically matching output. A very good one, but still.