How is that supposed to work?
Just look at what we have achieved in Earth vs. what we have achieved on the moon, or anyone's plans for a Mars colony. Mankind may set for on Mars eventually, but i don't think we'll ever do something like set off fireworks there.
Any colony that moves past the immediate survival stage is a success. That does not mean they have millions of years of fossil fuel stored to start further exploration.
Your scenario requires a uniformity of outcome across all the parts of that civilization, spread across multiple stars, and spread across all future time. They all have to go down and stay down.
So, if a stable multistellar society is not building colony ships, it's not because it can't, but because it has chosen not to. How does that uniformity of choice get enforced across time and space?
What you have are individual civilizations which may or may not, as you mention, decide to invest the time and resources into interstellar travel. But that investment isn't guaranteed. We've had the technology to send out interstellar probes for decades, yet we haven't committed to sending them out by the hundreds or thousands. We could have colonized Mars or the Moon by now, built Orion starships, but we haven't. Technology doesn't govern the advance of space travel, politics does.
>How does that uniformity of choice get enforced across time and space?
I think it's just a matter of probability. I don't believe technological development, much less to the degree of having a space program, are an inevitable result of intelligence or the presence of civilization. It's easier not to have a space program. It's easier, if you have a space program, to only explore your own solar system. Any number of issues, such as not being near enough to a colonizable star, not having sufficient energy or resources, natural disaster, giant ants, robot uprising, superflu, etc. could keep a civilization from starting, much less maintaining, a project of the necessary magnitude for the necessary amount of time.
And then you have to survive the trip, and actually succeed at colonizing another planet.
I think it's entirely within the bounds of reason for every civilization which has attempted interstellar travel to have failed up to this point.
They'd more or less evolve completely independently and it's conceivable that having these limitations will mean they never reach the same potential as the original humans did on Earth.
Usually the comparison with colonists of the past pops up. But they had the distinct advantage of being perfectly adapted to the planet and many civilizations still perished. Seeding another planet with humans raises a lot the bar for successfully developing a thriving civilization capable of reaching the levels required to further spawn successful colonies.
And a philosophical thought: would they even still be humans after (tens of) millennia away from the home of humanity, in vastly different conditions from the ones that evolved us? Would they be "our" thousands of colonies?
However, the economic cost of making an interstellar colonisation ship is so vast, that from where we are it seems reasonable to assume that anyone who does it has fully automated manufacturing and resource gathering – or, to put it another way, they are post-scarcity. If you’re post-scarcity, then you’re no longer fragile, because you can have a complete backup of everything you need, including the skills needed to rebuild.
Of course, there’s lots of ways for things to go wrong, and if I were to imagine badly written control software that means the fully automated manufacturing kills everyone, I’d be accused of being too derivative rather than implausible…
Also, we were able to land men on the moon 50 years ago, and now that knowledge is basically gone, and the tapes lost, and people are starting to believe the Earth is flat and that the moon landing never even happened.
Meanwhile, we can still read tax records from ancient Sumeria because they were carved into clay.
Complex systems are always more fragile than simple ones. It seems to me like we've been standing on a house of cards for the last century.
I assume that it will require population control, because we will not be able to find enough habitable planets to keep up with the growth we have today. Basically a choice of "immortality" or procreation. This will also set a limit to how many colonies that are practical to create.
Also some may not accept the risks of travelling to other solar systems. Why risk dying "young" when you can expect to live for thousands of years?
If all these long living people dont have to much new children (and might not be able to ? eq. if fully digitized or with body fully replaced with mechanical parts), it might be even easier.