Sounds more and more like its local to the head unit, I am thinking. Electronics are frustrating.
Phase 1. Take it out and clean up the terminals on the plug. Spray the dust and dirt off the guts with electronic duster spray. Put it back together and see. Low risk, but also a chance at redemption for the radio.
Phase 2. When it fails, leave the truck running and pull the radio fuse. Then put it back in. Does a hard power cycle change the behavior? You have already determined that turning it off/on at the power button will not do it.
If the fuse reset works, then you can rig up a toggle or push button to cut power to the radio momentarily. A bit janky for sure. But low cost. Not sure how the BCM will react to that nonsense.
Phase 3 is a new head unit at your preferred audio shop. That will fix it, assuming we are correct that the problem is in the head and now a downstream connector.
*Get a nice BT speaker and put it in the cup holder.
This old thread with a similar problem may help though. A speaker was grounding out on the door panel. You have not messed with the radio or speakers before, but worth ruling out.
Just bought a brand new Pioneer 200BT Touchscreen radio last week, installed it in a little over an hour. To give you a little insight on the install and myself, I am an electronics engineer, so of course, I soldered every connection and used heat shrink. I've installed many radios in my truck...