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In your statement, I'm not sure by which definition physically grounded things are a sufficient condition for being computable, but I think Penrose depends on the Turing notion of computability and the hardness of the halting problem.

We can of course move goal posts, redefine computability however we like, to get whatever conclusion we care for, but I think that Penrose effort is intellectually honest.

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Computing brain behavior is not the halting problem though. It's a computation of one algorithm.

Yes, just like the algorithm that decides whether any given algorithm terminates could be "one algorithm" (if it was possible) :-)

For that to be uncomputable brain must run the halting problem algorithm, which it doesn't, because the halting problem algorithm needs infinite memory. Being finite, brain has finite number of states, which all can be enumerated in finite time.

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