Given that Turing machines cannot be guaranteed to halt (and it's trivial to write an infinitely-running Turing machine), therefore humans are not, technically, Turing-complete.

Turing completeness is a theoretical construct that ignores that errors in execution inevitably occur during a sufficiently long program, due to the second law of thermodynamics (entropy must increase in a closed system). Any realization of a Turing complete engine eventually fails. That's different than halting, though, because it doesn't answer the question as to whether the program of the machine eventually reaches a halt instruction, when properly executed.

Well, I would say that any physical implementation of a Turing machine will eventually halt because you cannot guarantee an infinite energy supply. So if we're willing to ignore physical limitations then humans can be Turing complete - if not, then no machine be either.

How about a human population?

Oh, that too though we’re looking at it from a different angle. Most species so far have gone extinct though we’re a special kind, we may as well cause that without any external factors.