I don't understand why you think tracking user access rights would be infeasible and would not scale. There is a query. You search for matching documents in your vector database / index. Once you have found the potentially relevant list of documents you check which ones can the current user access. You only pass the ones over to the LLM which the user can see.
This is very similar to how banks provide phone based services. The operator on the other side of the line can only see your account details once you have authenticated yourself. They can't accidentally tell you someone else's account balance, because they themselves don't have access to it unless they typed in all the information you provide them to authenticate yourself. You can't trick the operator to provide you with someone else's account balance because they can't see the account balance of anyone without authenticating first.
Sometimes the potentially relevant list of documents itself is a leak all by itself.
You're competing with Google. The built-in Drive app does document scanning.