Strange Wire in Bathroom Wiring
This is an onward feed to some other stuff somewhere else in the house

While in the US, bathroom receptacles need to be on a dedicated bathroom receptacle circuit (that can feed any number of bathrooms), with the exception that you can feed both receptacles and lights for a bathroom off a circuit that services only that bathroom, there is no such requirement generally for bathroom lighting.  In other words, once the dedicated bathroom receptacle circuit is provided, the bathroom lights can be on a general lighting branch circuit. So, you'll want to put that "mystery" wire back with the incoming always-hot feed, lest you wind up inadvertently disabling some lights or outlets somewhere else in the house.