Firstly, I want to say it’s cool you’re positively engaging and stimulating a lot of conversation around this.

As far turing machines go - It’s only a concept that’s meant to show a fundamental “level” of computing (“turing completeness”), what a computing device can or cannot achieve. As you agree a turing machine could ‘simulate’ a brain (and we know brains can simulate a turing machine - we invented them!), then conceptually, yes, the brain is computationally equivalent, it is ‘turing complete’, albeit with some randomness thrown in.