Technology: How would you choose the right tech to ensure durability and stability over time. I imagine things would need to be upgraded, but things do degrade as well. I'm possibly thinking it may also offer a premium service to offer real cold storage to store digital material even to survive a global catastrophe. How should such things be stored?
How would you set up the organisation? Should it be non profit?
How would it be funded? I expect most clients would want to pay initially, but I also expect the clients and their organisations to have gone extinct before the 500 years are up. Ownership would probably be done via legal deeds.
How could a guarantee of at least 500 years be granted now if the organisation doesn't have enough funds to set everything up.
How would an organisation be established which could guarantee the mission from the start? Far too often we see noble and good technology companies get compromised over time. How can this be resistant to that? I imagine it would be running when I die, and when my successors die. How can I ensure, now, that the organisation continues with the same mission?
What would be the best way to set up the infrastructure to be resistant to political upheavals around the world, whilst still abiding by international laws? (e.g. copyright).
Digital donations must be accompanied by some monetary amount. All copyrights and intellectual properties (patents, whatever new nonsense is created in the future) tied to the donated information are assigned to the Order of Librarians in perpetuity. The Order of Librarians is authorized to use the donated information in any way they see fit that helps perpetuate the information (so selling access to it, placing ads on it, whatever).
And it must be a legitimate religious organization, with whatever rituals and hymns and methods and beliefs will be used by governments to decide what is or is not a religious organization. The central belief is something like the value of the documents is sacred and must be maintained.
And yet there is nothing you can do to guarantee any of this would last a century, let alone 500 years.
Look to the history of the Catholic Church, solely because it's one of the few (European) institutions that have outlasted various regimes over millennia. And even the Catholic Church has had "winners" and "losers" over the millennia, with various documents and books being retained while others have been intentionally purged.
You could probably warehouse the data in something like the world's seed banks - bunkers distributed around the world to preserve the genetic material. Technically you could even store the data similarly since there has also been research on DNA data storage.
The underlying basic idea is to just talk the customers into that. Usually it suffices. Heavy upfront investment tends to end badly, doesn't it?