There was a sci-novel about that, I don't remember who wrote it.
Essentially, after FTL got invented they caught up with generation ships and retro-fitted them with FTL drives; overall message of the story was that humans are a valuable resource and they should not be discarded lightly, especially in a mission to seed the galaxy.
Sometimes I'll be in an office building, or on a job site, or in a hospital room, or even just taking a big shit.
And I'll look around and think to myself "Everything here is man made. It all comes from people." And then I'll just kinda marvel at the productive and transformative nature of human beings.
In deep space, that only gets more true. The water you drink, the air you breath, the lights you see by - all the product of human enginuity.
I've thought about this too. A few apes, after a long string of evolution, figured out how to bang the right rocks together to make a television...or even a microprocessor. And that's just one piece of modern tech that some ape figured out, centuries after another ape wrote the complete works it Shakespeare.
… Sky's Edge, if I recall correctly. Except the “new tech” was not FTL (not a thing in Revelation Space canon) but the practice of ejecting a significant fraction of hibernating colonists and their supplies to buff their deceleration ability in order to hold higher interstellar velocity for longer so as to get a few years “edge” in lead time over other generation ships. All to enable the traitorous ship of the generation ship fleet to raid planetary resources sooner to build up military forces to raid the slower latecomers.