Aren’t we talking about a scenario where anyone left behind will die? That’s billions of people every time we hop planets. Am I missing something?

According to OPs rules, only Earth gets destoyed, planets we settle after that should be fine.

It’d be a nearly completely barren world with just a few crop fields. How inspiring.

Well, yes at first it would be quite bleak.

Or course we could also just cheat and use our FTL tech to time travel. Find a suitable planet, drop a couple of plant seeds, come back a few million years later and see what stuck.