Stability is achieved by having excess capacity, then limiting use of that capacity. Societies are not stable due to being right up at their limit; such societies collapse because of external changes push them over the limit.

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?

I don't believe there is, or can be, such a thing as a stable multi stellar society. Barring FTL technology, it's impossible to correlate activities or maintain coherent relationships when every interaction takes years, decades or centuries.

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.

There is some point to that. We are perfectly adapted to our planet because it formed us. Colonists on another planet may not find the same perfect conditions and it's likely that even to get a partial match (say Mars like conditions) they'd have to be many, many light years away from each other, with little outside support. And they'd need to adapt to colony ship life first, then to life on another planet.

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?