The earth will be uninhabitable in that time frame due to changes in the atmosphere and beyond that the sun itself will complete it's lifecycle.
I know there's a big fad to "just believe" in a SF future that spans space and time but physical realities in this area are pretty rough.
I think the best thing people could do is realise that, eventually, everything ends and believing otherwise when it comes to the human race is much like believing in an afterlife.
Imagine if you were an alien species who somehow comes across this capsule hundreds of millions or billions of years from now. It's proof of sentient life elsewhere! But then you date the U-238 and realize that they're probably all dead...
But, they've left all of their civilization, culture, heritage, and knowledge behind. And you get to experience that, even recreate a tiny simulacrum of their world. And it gives you something, it's a tangible form of communication and cooperation across aeons.
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In the short term, the backup is probably useful to have. Imagine if a collection is lost to fire or some other catastrophe, and one of the closer ones could be used to bring it back. Case in point, the fire at Notre-Dame. In 2015, Dr. Andrew Tallon, an art historian, painstakingly scanned all of Notre Dame, https://www.forbes.com/sites/trevornace/2019/04/16/we-have-b...
I think it's important to be honest. Would you have flagged his work as pointless in 2015? After all, the Cathedral has stood for centuries, been photographed so many times, what's the point of a 3D scan?
After 2019's fire, those scans became important (unsure to what degree) to the restoration effort. At some level, by capturing and preserving history, Andrew Tallon helped save history. And now it becomes a part of the story.
That's the goal. To engage in an act of optimism for the betterment of us and all of humanity.
We can barely get to the Moon and have no realistic prospect of making a self-sustaining Mars colony any time soon.
How is it credible to claim we can build starships that can cross lightyears without technological or sociopolitical problems?
The engines - which we're nowhere close to creating - are the easy part.
The real question is, is it worth making it a priority?
It will follow by itself once space mining kicks off.
That kind of claim needs an actual source, because it's not.
The distances are so many orders of magnitude too high for any of today's technologies, making this a pure daydream.
The best we could plausibly do is travel within Sol, and that's not starfaring.
It would have to be a multi generational journey in which any refueling/restocking is impossible and any slip up would cause a full wipeout.
Starfaring is far beyond us... and that's unlikely to ever change for humans with a biological body.
At that point someone can just put it on a thumb drive and take it with.
It's not beyond the realm of possibility that people ultimately inhabit a spaceship that wanders the universe looking for a new home.
We are doing that right now.
