We can manually execute the steps of a Turing machine. That's all that's needed.

It is so, trivially; humans wrote the find/replace box in Notepad++.

I mean, I can write a FSM that outputs the code for find/replace in Notepad++.

Yeah, but you can't write an FSM that can execute itself repeatedly over its own output indefinitely!

Turing's original idea of a "computer" was a human manipulating symbols on paper, so I would say trivially yes

We are guaranteed to halt, e.g lifespan. After death cells enter apoptosis stage where cells do final stages upon shutting down. I’d say it appears we are Turing complete, or at least it appears so from this angle

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.