A weird bacteria or nanomachine might convert everything to other weird bacteria or nanomachines. A weird virus can only convert all cells to weird viruses, since it needs cells to multiply. A weird prion can only convert other prions to their form, which is even more limited. Both of the latter scenarios can be very dangerous, up to an extinction event, but they're different from gray goo.
So, first of all, it's vague jargon to describe a hypothetical concept that does not exist and may not ever exist.
Second, the defining characteristic of "grey goo" is that it's of an artificial or synthetic origin, and hence, the "grey" part of the concept intimates technology, but not much else. The only other characteristic is that "grey goo" is typically depicted as a swarm of microscopic contraptions stuck on a runaway chain reaction, although the consumables that sustain the reaction can be anything at all. So, there's no real limit to the inputs or outputs of this hypothetical monstrosity, except that it's an all-consuming blob or nebulous swarm.
Third, you contradict yourself, since you ascribe microbes as grey goo, but then you tack on "non biological" sustenance as an afterthought. The microbial life at hand are not necessarily autotrophs or even consumers on non biological material, they are all heterotrophs made of biological material, eating each other. Furthermore the microbes are not "grey goo" because they are of natural origin and process.
In conclusion, grey goo is a thought experiment about a man made disaster or industrial accident, involving microscopic systems gone haywire. No other requirements are really specific to the idea.
Of course, I’m familiar with the term and its origins. Obviously bacteria were not created by humans, but they were a runaway reaction that ended up covering the entire planet and even deep below the surface. The early microbes were things like hydrogenotrophs (etc) that could feed on non-biological matter, although limited compared to the hypothetical technological version.
I was just pointing out the oft-observed notion that the development life itself (especially simple life like bacteria) was a kind of grey go moment, but is being held in check by viruses.
A weird bacteria or nanomachine might convert everything to other weird bacteria or nanomachines. A weird virus can only convert all cells to weird viruses, since it needs cells to multiply. A weird prion can only convert other prions to their form, which is even more limited. Both of the latter scenarios can be very dangerous, up to an extinction event, but they're different from gray goo.