Let's start at the beginning. Your post is drifting around a bit.
What symptom(s) did your XLR exhibit that encouraged you to make a dealership appointment?
Does your Adaptive Cruise Control system operate correctly?
Does your Infotainment system (Radio/CD player/DVD/Navigation) operate correctly?
Does your dealership have a Certified (this means they attended a special XLR-specific course, not the standard ASE rating) technician? Are you seeking help from a Cadillac dealership?
The Adaptive Cruise Control Gap switch is wired directly to the Body Control Module, not the radio.
What "module" is being identified as faulty? There are many modules in this car, so the technician should be specific and identify it by part number on the repair invoice. Any DTCs (trouble codes) should be identified in writing.
When a new radio is installed, it must be paired to the VIN of the car using a Tech 2 (or TIS) or it won't work at all. If it was working, that had to happen.
If your only problem is a loss of Voice Command operation, there are a few other areas to verify, but the Infotainment system does process some switch commands from the steering wheel.
Voice Commands use the steering wheel-mounted switch to activate the function while spoken audio is routed from the microphone (shared with OnStar) to the Navigation System. Voice commands are processed, performed, and confirmed by the Navigation System.
CC