If you have access to the kind of energy that enables interstellar travel, you also by definition have enough energy to terraform your own planet and keep recycling resources indefinitely.

If you have infinite energy, your planet never "dies out", because you can terraform it at will.

No amount of terraforming will save the Earth when the sun dies and takes out half the solar system with it. There are other dangers too that make it irresponsible to leave all of humanity on one planet. Our survival as a species depends on us being able to survive on multiple worlds in multiple solar systems, or at the very least being able to sustain ourselves on interstellar ships.

It's unlikely that humans exist then. Speciation or calamity will intervene.

I'd like to think we could make it, but if it isn't already too late, we'll have to stop poisoning ourselves and the planet we have first to stand a chance of getting past The Great Filter