Please read the thread carefully. You're fundamentally misunderstanding the context of this discussion. We aren't talking about interstellar travel in general. We're talking specifically about the utility of using interstellar travel as a means of keeping exponential growth going forever.

The species can keep growing by extending out to the stars, but an individual star system can't. Eventually your star system reaches a maximum population. In the age of European imperialism, Europe shipped its excess population off to settler colonies Australia and the Americas. That will never be possible between star systems. In the 1800s, Britain could lower its resource demand by sending people off to the Americas. It took far more resources to keep a person alive for their lifetime than it did to send someone across the ocean. But you save no net resources by shipping someone off to Alpha Centauri. Sol will not be able to solve an overpopulation problem by shipping people off to distant Suns. And it's not a matter of how much cargo you bring with. The energy required to move just your body across interstellar distances dwarfs what is required to keep you alive for many lifetimes.

So, no, population cannot grow forever. Eventually Sol will have to stabilize its birth rates, or it will have a problem. Starting new seed colonies around distant stars can probably be done. But it won't allow the population or economy of a single star system to keep growing forever. With interstellar colonization, you're not expanding your civilization to multiple star systems, you're budding off new independent civilizations around those distant Suns.

A seed is actually a perfect metaphor for interstellar colonization. A tree can throw a seed to the wind to make new trees far away, but those seeds don't help that original tree grow any bigger.