Are there any auxiliary buttons on the controller with unassigned functions that can be used to control other wireless components or perform special functions?

The pairing button located on the bottom of the controller handles two tasks.

One, it pairs with the derailleur and you can reference the pairing instructions/video for more.

Two, the function of the pairing button is to trim the rear derailleur (taking the place of the barrel adjuster) see the adjust/trim instructional video for more.