If the Universe is computable, then human thinking is computable. All due respect to Penrose for his stellar achievements, but frankly the implications of Turing Complete, the halting problem, Church/Turing hypothesis and the point of Godel's Theorem seem to be things he does not fully understand.
I know this sounds cheeky but we all have brains that are good at some things and have failure modes as well. We are certainly seeing shadows of Human-type fallability in neural nets, which somehow seem to have a lot of similarities to human thinking.
Brains evolved in the physical world to solve problems and help organisms survive, thrive, and reproduce. Evolution is the product of a massive search over potential physical arrangements. I see no reason why the systems we develop would operate on drastically different premises.
My peak programming skills are close to what they were 30 years ago, but I cannot sustain that level of concentration for long periods as I once could.
I feel like a pinch hitter: I can do a couple innings at a high level of performance, but I can't keep that level up as long as I used to.
OTOH I think I have better judgement when it comes to deep, complex questions of long-term architecture choices. My "meta-programming" skills are sharper than ever.