I need to investigate this further when I have more time to do so. But it seemed like the Pro Controller was not being recognized in the same way that the Joy-Cons were. Strangely, the input buttons on the Pro Controller still were visible in the Input Debugger and worked correctly (i.e., no random values), but otherwise Unity wasn't acknowledging the controller was connected.
I need to investigate this further when I have more time to do so. But it seemed like the Pro Controller was not being recognized in the same way that the Joy-Cons were. Strangely, the input buttons on the Pro Controller still were visible in the Input Debugger and worked correctly (i.e., no random values), but otherwise Unity wasn't acknowledging the controller was connected.