Start with a hand-wavy definition of consciousness. Move the goal post whenever your stated prerequisite of consciousness is reached and resort to unfalsifiable assertions about qualia.
And throw in some category errors while on it: when you're talking to Claude, you're not actually calling a stateless LLM directly, you're talking to an AI system (and yes, that's often just three LLMs in a trench coat). But claims about the topology and workings of a single LLM are as relevant to the question of consciousness as claiming that humans can't be conscious because the limbic system doesn't technically support it.
Coincidentally, I just attended a fantastic conference on machine consciousness (https://machine-consciousness.ai). It's a fantastic place where literally all speakers disagreed with each other, and yet found an incredible amount of common ground.
It shows that the LLM part found ways to mimic human conversation with a mechanism that is not the same as a typical biological brain. Then, you can push the AI system on adding things on top, but it is too late: these things on top will have no incentive to recreate from scratch the mechanism. The LLM pushed the system into a local minimum, and the rest of the system will not "go into a dis-optimising direction and restart from scratch".