Without knowing the “higher” reality, I’d still call it a simulation. An emulator is capable of replacing the “real” system it’s emulating. Maybe that’s your view on the topic, but I find it more likely the higher reality is more complex than ours because it contains ours. Therefore our reality could not be an emulation. Lots of speculation though.
I don’t have a specific recommendation (I could just give out names of tools that seem to match your needs but I can’t really say I’ve used any), but in your place I’d reconsider your last requirement of “no connection to the DB”.
In my view the best docs are the ones that take the least effort to keep up-to-date. Consider a tool that’s able to dynamically list and extract schemas from your existing tables and generate a nice HTML or diagram that can be used as a quick and up-to-date reference. That will require little or zero maintenance compared to a manual diagramming tool. So I’d start looking there.
Depending on the project and usage I’d also consider exposing the database through an API. This makes documentation much easier too, as there are tools to auto generate API docs and you’ll decouple your DB schema + access from its usage, which has its own benefits.