And a lot of the survivors from Earth would head over to Mars to overwrite your backup.
It’s always been unclear to me how much a Martian civilization would improve humanity’s odds of surviving Seveneves, what with humans being involved and all. I think it’s the article of faith I’ve seen the least substantive critique of— maybe because it’s so depressing to think critically about.
BTW, on this note I can recommend The Ring of Charon[0] and its follow-up books. In this case, its Earth suddenly vanishing due to some ancient alien technology being activated by mistake. The book then follows the consequences for the advanced but still partially Earth dependent space habitats in the Solar system as well as people on Earth figuring out WTH their planet has ended up and why.
The open question I have is does a planetary colony help per se, once the technical problems have been solved on an emergency basis, and what’s left are social problems which are far too late to cure?