Back when the word "nanotechnology" used to mean itty-bitty robots* rather than some extremely fine chemical processes done in sequence, or extremely small particle size, I had wondered if we could get to the point of said itty-bity robots before all of the brilliant people who made playable games for restricted consoles like the Atari had retired.
* More specifically, miniaturized robots consisting of one or more robot arms with multiple degrees of freedom, a CPU, some kind of storage (perhaps something like wound-up DNA serving as tape on reels), executing programs written by humans.
That concepts sounds like fantasy, cells are shaped like cells because 'itty-bitty robots', and most other configurations, don't work thermodynamically or physically or chemically at such small scales.
Cells are shaped like cells (which is to say ugly bags of mostly water) because they are self-perpetuating chemical reactions in solution. We usually conduct our chemical reactions in vessels that are round along at least one axis, maybe almost two for our round-bottomed flasks. This is natural because we're enclosing a maximum volume of our solution with a minimal surface (cell membrane or borosilicate glass).
On a macro scale, life tends to be bilaterally or radially symmetrical, but our robots are not necessarily like that, just considering even factory robots which are often an arm and little else. So, at the micro scale, I don't think they have to resemble "life" there, either. I'm hardly suggesting some kind of tinkertoy with one atom here and another atom there and the strut being, instead of wood, a covalent bond. No, I think we would need more atoms than that.
Frankly, we haven't much tried to scale down our robotics. Oh, you'll find someone who will produce the flagellar motor (a mere forty-five nanometers, compared to the ten thousand nanometers of a human cell) but not much else. I wouldn't worry about the thermodynamics and quantum effects until we're down to that motor level.
Do you realize you can determine this for yourself, right now?
By just taking standard equations found in textbooks, plugging in some numbers, and realizing that things such as Ideal Gas Law don't hold at such scales.
You can even derive the equations for yourself to confirm your not being misled by the textbooks, but that takes more skill and knowledge then is likely feasible to acquire without advanced study.
Fortunately, I have a physics degree so I am quite sure I am not being misled by the textbooks.
We will face different challenges at different scales, of course, but even as recently as 2016, researchers using a scanning tunneling microscope crafted a 8,192 bit message using less than ten thousand atoms. So, no, I see absolutely no reason why we couldn't have robots within an order of magnitude of the human cell -- we have bacteria which are much much smaller capable of a variety of functions as well as reproducing themselves
You might look into Feynman's "There's Plenty of Room at the Bottom."
* More specifically, miniaturized robots consisting of one or more robot arms with multiple degrees of freedom, a CPU, some kind of storage (perhaps something like wound-up DNA serving as tape on reels), executing programs written by humans.