Which is just one of many bad assumptions in how people do these calculations. At a minimum you don’t get a straight path from A to B. Assuming any kind of limitation in distance traveled and your at the mercy of the distribution of whatever resource you need. Aka need rocky planets with liquid water, that’s likely going to be an very indirect path. Even just non binary star systems is significant. Further, assuming every trip is successful is again unlikely. How long you need to wait before the next trip is again a major qualifier.

For example, what happens if they first send a probe to verify habitability? Suddenly travel times more than double.

I have seen plenty of optimistic calculations that still add up to over a billion years before total colonization and sometimes much much higher than that. And that’s a billion years where expansion is a major priority at the frontier. Look at successful colonizations that don’t expand rapidly and again things keep slowing down.