> Literally the whole universe, including your brain that exists within it, is to our current knowledge a Turing computer
A Turing machine is an abstract mathematical model that is not, as far as I know, physically realizable in the finite universe. A human brain cannot "be" a Turing machine.
"Behaves like" or "can be modeled by"? Possibly, although still not proven. But it cannot "be" one.
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.