The privacy policy for Orion for Reddit is really simple.
Simply put, Orion does not transmit any data to me. I don't want it.
Everything you do in Orion is a direct interaction with Reddit servers.
Logging into Orion is like logging into Reddit from a web browser. The cookies that you receive during login are then used in Orion's general web session the same way a web browser would to request Reddit's json endpoints.
Account switching works by having different WebKit containers (kind of like different browser profiles). Each one is securely stored on disk.