This is the usual blurring of lines you see in dismissals of Penrose. You call the argument "unsound" as if it contains some hard error of logic and can be dismissed as a result, but what you state are objections to the assumptions (not the reasoning) based on your qualitative evaluation of various pieces of evidence, none of which are conclusive.
There's nothing wrong with seeing the evidence and reaching your own conclusions, but I see exactly the same evidence and reach very different ones, as we interpret and weight it very differently. On the "existence of a physical process that cannot be computed", I know enough of physics (I have a degree in it, and a couple of decades of continued learning since) to know how little we know. I don't find any argument that boils down to "it isn't among the things we've figured out therefore it doesn't exist" remotely persuasive. On the achievements of AI, I see no evidence of human-like mathematical reasoning in LLMs and don't expect to, IMO demos and excitable tweets notwithstanding. My goalpost there, and it has never moved and never will, is independent, valuable contributions to frontier research maths - and lots of them! I want the crank-the-handle-and-important-new-theorems-come-out machine that people have been trying to build since computers were invented. I expect a machine implementation of human-like mathematical thought to result in that, and I see no sign of it on the horizon. If it appears, I'll change my tune.
I acknowledge that others have different views on these issues and that however strongly I feel I have the right of it, I could still turn out to be wrong. I would enjoy some proper discussion of the relative merits of these positions, but it's not a promising start to talk about throwing things in the garbage right at the outset or, like the person earlier in this thread, call the opposing viewpoint "stupid".