The Encyclopedia Galactica will be unable to detail the life history of everyone who ever lived, but the Earth's composite knowlege of gardening, cooking, crafts, science, etc., can probably be stored rather succinctly. AI programs will be available to extract information for any particular purpose and reformat it for any audience. Accuracy will be guaranteed, within the limits of the target vocabulary. I think that's worth working toward. It seems to me that our ability to produce information has far outstripped our ability to catalog it, and in the absence of any better algorithm we all simply discard whatever does not seem likely to be of future value as a resource.
Libraries have to do some kind of pruning or ignoring.
The idea that cellular refers to the power source is absurd. While it depends on what sort of implicit or explicit agreements are in place, it is generally the case now that an employer has the right to examine all employee files on a computer the employer owns. It is not even like stuff locked in your desk since the employer does not need to bypass any locks to just take the physical disk packs or whatever and print out every bit on them. If you are worried about this you should, at a minimum, encryt anything that is sensitive in this context. They developed a set of categories for keeping track of the incidence of such events.