This is literally the Hard Problem of Consciousness leaking out of the machine.
There are three possible scenarios for how this ends:
1. People widely attribute consciousness to AI because it appears conscious. 2. People discriminate based on physical properties: organic beings are conscious, digital beings are not, even if they appear conscious. 3. Consciousness is an illusion and nothing is conscious, not even humans.
We might even cycle through all these scenarios for a while.
This is already happening, and it's really terrifying. Wait until AI starts accusing people of crimes...
to be fair it will easily confirm any suspicion for the reasons you laid out, so even if you have no technical knowledge just a bit of interrogation will break the parlor trick.
I honestly think this has little to do with the tech itself but that these are the same people who think the phone sex worker or the OF creator loves them or that the Twitch streamer they like is their best friend. 'Parasocial' is a bit of an overused word but here it literally applies, this is a kind of self delusion in which the person has to cooperate. Mind you this even happened with ELIZA back in the day too.