My '04 Ford T’bird is set up so the radio continues to play after you turn off the ignition and even remove the key from the ignition. As soon as you open a door to exit the car, then the radio shuts off.
Are your interior lights coming on when you open the driver’s car door? If no, perhaps the switch in the door jam is defective. If the interioir lights operate properly when doors are opened and closed then your radio could have a defect if it stays on. If you can turn it off manually that’s what I’d do. Trying to fix it could cost a bunch of money for little benefit.