Nikolai Kardashev created the Kardashev Scale to characterize civilizations by how much power they use—from a "Type I" civilization which captures all the solar energy falling on their home planet, to a "Type III" civilization which captures the whole effective power of a whole galaxy. In the early 21st century, we are far short of even being "Type I" (so we're effectively "Type 0"), but the future story we imagine for ourselves is exponential growth. Population has grown by, say, an order of magnitude in the last 400 years (from 800 million to 8 billion, give or take), so we should only need some 10,000 years to get to "Type III" when we simply assume continued exponential growth.
future-physics warp drive, it is optimistic to think we could
cross the galaxy once in a million years (at .2c, say), so somewhere in the
next 10,000 years our exponential growth has to stop, constrained by the cubic
way that light cones work.
A variant of this "we must expand" directive is assumed by the Drake Equation: a long-lived civilization is, by definition, so big it can't help but "leave its mark" on its containing galaxy in the form of radio signals, if nothing else. Superficially, it seems there should be many such civilizations, and they should be easy to detect if they are hard-wired for exponential growth like us, since they and their artifacts should be literally everywhere.
The Fermi Paradox, then, invites us to explain why we have no evidence of these other civilizations.
I think the answer is simple: Exponential growth, like a viral infection, is unstable. Whether it's on a scale of 10 or 400 generations, there is a final wall (a "great filter", in Fermi's terms). Only growth that is polynomial or less is sustainable on million-year timescales, particularly if (in a galaxy full of life) you actually bump fairly quickly into another civilization with a moral and/or de facto claim on the resources in some other region of space.
So we end up with a galaxy that looks like a Liu's The Dark Forest: quiet civilizations growing in volume and power consumption not at all, or only at logarithmic rates. Any hint of exponential growth, or possibly even polynomial growth, would require a response. For all we know, such a response was set in motion circa 1800 (when the atmospheric changes of the industrial revolution could have been detected) in the form of a diverted near-earth asteroid, scheduled to hit around 2100.
There must be a story in this somewhere, here's one sketch: Circa 2100, the earth's surface was rendered uninhabitable by asteroid impact. However, the nascent Mars colony and some orbital habitations survived, and by 2240 are on somewhat stable footing and ready to restart exponential growth through the solar system and into the Oort cloud. Society looks like we think it should: multicultural, accepting of all genders and sexual identities, egalitarian, access to health care, etc. Our point of view character will be a young person just coming of age in the largest city on Mars, presently on a solo tour of the solar system to rival Golden Age science fiction.
While flying by some geologically interesting moon, our narrator's ship is struck by some matter ejected from the surface. This matter forms itself into a duplicate of our narrator, and at length they learn to communicate. Let's call the alien Alice and the narrator Bob, just to make everything simpler.
Just like Bob is coming of age in the human society of Mars, Alice is (was) coming of age in their own society. Alice's society are also a bunch of exponentials who evolved in the upper atmosphere of Jupiter. But their philosopher-scientists saw the trap of exponential growth and found a solution: They adapted themselves to live at ever-slowing rates, most recently building organic computers to survive deep in the atmosphere of Jupiter, simulating a society of a trillian Jovians at a rate of about 1 day per 1,000 real-time years.
Alice, having accelerated themselves to realtime (and beyond, when they were learning Bob's language), is considered a criminal in their society and can never return without facing the punishment of being slowed all the way to zero until they have paid back all the time they "stole".
At risk of becoming too didactic, Alice tells Bob everything that is known about different societies: The exponentials, who mostly flash and fade; the polynomials, young races who may yet adapt and last; the logarithmic, long-lived civilizations who form the backbone of galactic governance; and the rumored constants, who long ago disappeared, perhaps into quantum computing devices made of dark-matter.
In any case, Alice tells Bob that if they continue to display exponential growth as a species capable of space travel, there will be terrible and large-scale retaliation from galactic culture, such as the catalyzed supernova of Sol itself; as Alice's species would end up as collateral damage, the Jovians would be in the unfortunate position of having to commit genocide against the humans first, just for self-preservation. Presumably some mid-level Jovian military types are also (lawfully) accelerated to real-time to monitor the situation.
A narrative discontinuity, and Bob is recovered from their wrecked space ship, with no sign of Alice (or is it the other way around?). Here ends the novella.
If the story should continue, we might see Bob trying to effect political change among the humans, or hear the problems faced by Alice's species' scientists, who have the eternal problem of growing their computing capacity with ever-decreasing subjective time creating impossible deadlines. (Or are the scientists lawfully accelerated, like the military?) How about drawn out parliamentary scenes where the logarithmic species debate how to deal with the infestation in Sol System? Or perhaps we go on a wild goose change for the vanished constants, believing they have the secret of zero-point energy or the like.