Wasn't expecting to find enough for later simulations or find out she was President of Earth or anything, or even much detail. Just some sort of 'ended up marrying the bf (or not), children, age/cause of death, whether she ever made it as a singer', that sort of thing. Assuming no random 'WW3 that fragmented the records' excuse like TOS used, most of that should be public record and could have survived. It's harder to do today because digital is fairly new, but people can trace basic genealogy today back hundreds of years (or more in some cases). If we're only trying to go back to 2015 (yes, plus 400 years, so time and loss of records is a factor), we're starting with digital records as a baseline, so much more likely to still exist into the future.
Given that the crew seems to be 2000's pop culture junkies, seems like a lot survived from that period. Didn't need a drawn out scene of the rest of her life or aging, any of that, just a 30 second clip of Gordon doing some digging, finding out she made it as a singer, ended up marrying the guy that she "dumped" Gordon for, lived to be 85, that sort of thing. Allows the scene some closure, so that he finds out how the story turned out without him instead of just quitting once he realized he couldn't have the real thing and it was wrong to game the simulation and ruin what was real about it.