So, let's say about 150 years later, this isolated rogue human colony develops 1950s level technology
First of all, whatever the originator planned for (even possibly including a Safehold-level religious control), the colony has to know they are human colonists from somewhere else and have a good guesstimate about where. If those data were included in the original ship's cargo, they knew from the very beginning. Otherwise, it would quickly become obvious anyway.
- no fossil record with the human Bauplan found
- planetary biochemistry is visibly "hacked together"
- bioweathering and other indicia point to the colony not being older than 150-300 years at most
- technology started from a way higher level than you'd expect
- no archaeological remains of earlier settlements anywhere
- oral tradition still easily goes back to Landing Day, but no further
So, "we came from the stars, already pretty advanced". Which star? In 1950 the local G-class stars of our neighbourhood were acceptably mapped. I'd expect no less from the colonists. "If we arrived here, our Sun must have been visible from the mythical Home; it follows that Home's Sun should be visible from here".
So the colonists would build radio and optical telescopes, with a much keener spirit than ours was, and would point them to nearby G-class stars, which would be exactly the most likely to host the recently established Human Federation of Planets.
It's just a matter of time before they detect radio waves and laser light from those sources.