"Biological," too, is well defined. It relates to living things and their processes.
> Why do the machine parts in biology show such flexible application?
Evolution.
> A gear cog won’t ever moonlight as a signaling chip
A gear cog was purpose built for that purpose, but you will find that people often recycle parts into other systems, often in completely different roles.
> How is the biological machine able to build itself?
Protein synthesis.
> What does self assembly imply for the machines function?
The way that a machine is built has no bearing on how the machine functions. I could build the same machine using a 3d printer or a CNC router.
> Where does this machine get its inner drive?
Evolution selected for organisms that survive long enough to reproduce. Different biological systems handle this differently.
> No LLM has been found that starts outputting text unprompted.
If you give an agent a goal, it will perform actions to achieve that goal. This is just as true for artificial agents as it is for biological agents.
> Why is no manufactured machine able to do this?
Many do. Even robotic vacuum cleaners will charge themselves without human prompting.