General Tile Discussion

Hello. I am trying to run wire for a bathroom fan. The walls are down to the studs and I am trying to run a wiring that is needed before putting up drywall and foam board. I am not replacing a bathroom fan so I have to run new wire. I thought about running a new black/white/ground wire from the breaker box, but it would be difficult fishing the new wire down to the breaker box without opening up additional walls or ceilings. So I am trying to see if there is a way to use existing wire/outlets in the bathroom. I have attached pictures as reference. The single switch you see on the wall controls the gfi outlet and the vanity light that is across the room on the opposite wall (see picture with outlet and vanity light receptacle). The romex wire coming from the top of the single switch goes up through the top plate and across the attic and down the opposite wall top plate, connecting to the vanity light receptacle and then the receptacle connects to the gfi outlet. The romex wire going from the bottom of the single switch goes over and connects to a gfi outlet on the other side of the wall (this is the bedroom wall). The wire then continues from that outlet receptacle to the corner of the unfinished bathroom and disappears. How can I connect to a new fan? The fan has a touch screen switch. I also need to keep the single switch in the picture as that controls the vanity light. I do see there is an open spot on the gfi outlet in the picture with the vanity ligth receptacle. Not sure if that is useful. I have also attached pictures of the LED screen switch and the wiring diagram for the fan. I would really appreciate any help. This is keeping me from moving on in the project.