> I could say that the rock is falling because it has a purpose - it's trying to achieve the minimum potential energy. What's the meaningful distinction between that and a plant?
The difference is that plant cells are not moving in a way that minimizes their potential energy, they are performing simple computations, individually and at the plant level, to decide if they should divide more in certain areas of the plant than in others according to a strategy encoded in their genes. They do this in order to achieve certain kinds of exploration patterns; there are also basic signalling mechanisms in the plant, so that when a particular root has found a source of nutrients, it will preferentially grow more than other roots that haven't, so that the amount of nutrients in the whole plant is maximized. This requires several layers of (simple) computation, both at the individual cell level and at the whole plant/root system level in order to achieve.
The rock is not doing any computation, and every segment of the rock is acting entirely independently from every other - in fact, there is no clear-cut definition of where one part of the rock begins and another part ends, or even exactly where the rock ends and the air begins - each molecule is completely individually acting according to the forces acting on it.
> is it the plant as a whole that's "trying to find nutrients", or is it individual cells or groups of cells within the plant? With many plants, you could reduce it to tiny bits of the whole, and those tiny bits will still try to grow roots.
It's the whole plant, which is an interconnected series of individual cells. If you separate one plant into two, you're right that both parts will continue growing roots, but the pattern will be different if the roots are part of one plant or two separate plants, even if they are clones of each other.
For example, say that you have a plant in the middle of a pot. On the left side of the pot you have a lot of nutrients, on the right side, very little. The plant will start growing its roots uniformly, but will relatively quickly start favoring the left side of the root system, and the right side of the root system will stagnate. If you then cut the plant into two right down the middle (assume we can do this without killing it) and insert a solid separator between the two. The right side of the root system will start growing a lot more, and likely it will end up larger than the left side (since more expansive roots are needed to absorb enough nutrients in the poorer soil).
Telling the difference between one organism versus its constituent parts is not actually very hard at the micro level. It is true that in some sense each individual cell is an agent in itself in its environment, even in an animal; and perhaps even each individual organelle in a cell is the same, but they are also very clearly working together and communicating in a way that simple physical forces can't explain (e.g. its very clear that animals are not pulled towards food by some food-gravitational force - they have to actively explore the world to find their food, in a computational way).
This also means that you can choose to analyze this at any level you like. Is a bee a singular organism, or is the colony the actual organism, the bees more akin to organs of the colony? How about humans in a tribe - are they separate organisms or organs of the tribe? Both are true to some extent. Just like cells and organs act as agents in their own environment, so do individuals act as agents; but then, so do colonies or tribes at a higher level.
> Maybe we really are just arrangements of broadly independent components, each with its own "purpose" (ultimately boiling down to physical processes), which communicate to create a delusion of self because that's what their individual "purposes" effectively added up to?
Again, we can quite easily observe that the behavior of, say, a worm is not reducible to the behavior of each individual cell inside the worm. We have even analyzed a very simple worm in some minute detail [0] and can say pretty clearly where individual decisions are made, and how they are propagated to other cells (here decision should be understood in the broad sense, like how a binary search algorithm decides whether to search the left or right side of the list; not the emotional human sense, like Sophie deciding which child to save).
[0] https://en.wikipedia.org/wiki/OpenWorm