This is a weird one. Factory radio that was never modified. All the sudden the on/off button won’t turn on or off the radio. However, when the truck is running the radio is on. Turn off the ignition the radio goes off. Volume controlled by same knob works fine. Glad it turns off with the ignition but not sure what is happening here.
Your on/off button is broken and stuck ON. It is probably a momentary contact switch. The car removes the power to the radio when you shut it off.
I don’t see a problem here. Live with it. If you don’t want to listen while truck is running, turn the volume all the way down. The alternative is to buy a new radio.