We have the most extensive data available for recent years, though. Ice core samples are also nothing new, they've been extensively studied for decades. Many of these cores are carefully removed and placed in ice cold storage warehouses: https://qz.com/1590747/an-antarctic-ice-core-may-show-1-5-mi...
Again, the physical ice core samples are permanently kept in giant freezer warehouses. And we know how to store binary archive data for thousands of years securely.
In 10000 years the earths crust moves warehouses are destroyed. The discovered binary has to be decoded and translated. Humankind has changed, evolved or devolved in ways we cannot yet know. Looking forward from now the two proposed future reality are equally valid. We have no way of knowing that outcome.