I tried to pull your wiring diagram but I forgot BMW AG shut down New TIS.
Here is the document link I used and it is for 2001-2006 but you will need to see if you are prewired. 12V and GND wouldn't be too hard to run from the fusebox if needed but check and see if you are prewired. Page 5 of this document shows how to confirm.
https://xoutpost.com/pdf/Heated%20wheel%20retrofit.pdf