I’m betting your house used to have a 2nd bath or was going to get one but was abandoned. The fan was likely the bathroom 2 or possibly a range hood.
All brown wires is definitely what’s incorrect. Hot, neutral and ground should be easily identified at a glance (black or red for hot, white for neutral, green or bare copper for ground where I am). I’ve only ever seen brown sheathing on older fabric or paper insulated wiring.