I am replacing a ceiling fan in a bedroom and the wiring in the receptacle is confusing me
Take your fan controller back and get a Lutron MA-LFQM instead

Most fan controllers on the market today are incompatible with your wiring configuration, where there is only one hot going up to the fan from the switch.  However, there is one that's suitable, and that's the Lutron MA-LFQM.  This uses a module in the fan canopy to decode a digital signal from the wall controller into separate fan and light outputs, and isn't too hard to find.  (It also can use matching Lutron accessory controls for 3-way or 4-way work.)

Once you get the correct control in, you'll want to pick one of the bottom hot/neutral pairs and stick with it, capping the other incoming hot and neutral off individually.  Once you do that, the control is wired according to the single-pole instructions, with the load neutral nutted to the remaining neutral, the line hot connected to the black screw on the control, and the load hot connected to a brass screw on the control.

At the ceiling fan, the canopy module is wired with its white neutral to the remaining neutrals (fan-neutral and incoming-neutral), its black to the incoming black (switched-hot), its red to the light kit wire off the fan (typically blue), and its yellow to the fan wire on the fan (typically black).  Connect all the bare/green grounds (fan ground, box ground, incoming ground) together, button up both boxes, turn the breaker on, follow the control activation procedure in the instructions, and enjoy your fan!