Are there any well thought through stories about what this would look like? For example, I'm thinking about like nutrient flow, decision making, energy input, gravitational force, things like that seem to govern the value and speed of intelligence.

Hard to avoid spoilers here but Vernor Vinge hits on pretty much exactly this in A Fire Upon the Deep. Though he's interested less in the hard sci-fi aspects of how/why and more on the consequences of it (story-wise).

For the opposite, "Dragon's Egg" by Robert L. Forward is a fantastic read

I think this is a slow version of the quandry behind Quantum Computing: how do you distinguish events from the noise floor? It happens in the quantum context and it would happen in the millenial timeframe completing "operations" which have to be compared to e.g. the stability of orbit around a sun.