Finite machines are a subset of all possible Turing machines. Every implementation is a "be", Turing machine is a mathematical concept. Your laptop is one, many things accidentally become one (eg C++ templates). The universe as best as we know is one. Whether you prefer modeled by one or is one, the fact is, to our current knowledge, the workings of the universe doesn't need anything more powerful than a Turing computer, and the equivalence principle states that all Turing computers have equal power of computability. If the universe is, as is most probable, finite, then things become even easier, that should be a more manageable class of Turing computers than the set of all Turing computers.
I don't necessarily disagree, although there's a lot of "ifs" and "to our knowledge". The main thing I disagree with is identity.
If you want to claim that the evolution of the universe can be modeled using a Turing machine/finite state machine, that's probably not terribly far fetched, and I would somewhat agree. But it's a large jump to say "can be modeled by" is equivalent to "is one".
Various physical processes can be modeled by equations, but the rock falling down the mountain isn't an equation. A swinging pendulum isn't an equation. Code modeling a bridge is not a bridge. Ceci n'est pas une pipe.
I hold the view that various models and approximations are just that, and try not to confuse a successful model for what the underlying reality is.
And getting back to the question at hand, even if our brains can be modeled by a Turing machine, and LLMs behave/can be modeled like Turing computers, still does not mean our brains are equivalent to LLMs.
(Note that I'm learning a lot from these debates, even if I disagree with a lot of people. I've started down a more philosophical route and they do get me pondering)