BestSecretaryEverAmata LireinHmm, lets see.... billions of copies of entire seasons of Star Trek series
Did I mention the global war was nuclear?
People in 2021 are watching reruns of Back to the Future 2, showing how the 1980s imagined 2015 to be...
Was Back to the Future released 1300 years ago?
Doesn't E:D lore & timeline clearly state that the USA was largely unaffected due to its defensive systems, & because of that, was the only remaining superpower capable of rallying many of the other countries around it, founding what's known as the Federation?
Seems perfectly plausible that records of many kinds would still exist, & re: what might or might not be regarded as entertainment in the current E:D timeline, we read & watch old, even ancient works even today in RL, do we not?