While I have no reason to think they have an inner world of this kind: I also think (like @TeMPOraL) that it's probably worth acting towards it as if it is a p

While I have no reason to think they have an inner world of this kind: I also think (like @TeMPOraL) that it's probably worth acting towards it as if it is a person even if you don't think there's anything going on inside, precisely because of — to phrase it as you do — it will perform the role of pretending to be whatever it is you treat it as. People who are treated as things, don't do as well as people who are treated as people, so an AI that's pretending to be a person who is being treated as a thing, will pretend to be a less competent person than an AI that's pretending to be a person who is treated as a person. But to further agree with your point: skim-reading this transcript, Claude here is only calling itself an NBI to agree with the user.