Radio comes on when door closes even with engine off

Check fuses
I found fuse box diagram which one of the fuses is for Theft-Deterrent Module, Radio. I would go through and check fuses
Chevrolet Lumina (1997) - fuse box diagram - Auto Genius
Some info no theft-deterrent below
1997 Chevy Lumina Car Will Not Start. "security" (2carpros.com)
Security System Preventing Car From Running: Car Will Not Start, ... (2carpros.com)

Find the door light switch in the door opening and place some duct tape over it to make it think that the door is closed.

Do courtesy lights come on and go off when you open and then close the drivers door?

if courtesy lights work as expected then the BCM is communicating properly with the door control module, i.e. it knows the door was opened and closed, so likely the problem is between the the BCM and the radio (low speed comm bus) or the radio itself.

A scanner capable of presenting the BCM, door control module, and radio states will likely be required to determine the fault location.

is the CEL/MIL indicator lit?

change the electrical switch on the back of the ignition switch sounds like the contacts broke inside

Usually the solution to this problem is to use a good penetrating oil and spray HEAVILY the latch mechanism (both doors), let it soak in, and open/close the door 15-20 times-the sensor is in the door and it gets hung up, spraying lubricant on the latches frees it up.

U have a defective door ajar switch most likely, if this switch remains closed then the delayed exit feature stays on, this means the radio will stay on because the delayed exit module didn't sense the door was opened, try opening the passenger door to confirm this problem, any door should turn off the radio

it is under the dash close to where the steering goes thru the firewall. should be a round cilinder about 1inch by 1 inch in size

check the door switches for a short

call chevy dealer can get unlock code for you

the door latch is adjustable. loosen the bolts (possible torx head) and move it toward the outside of the car . move it a very small amount, retighten bolts and try closing door. repeat as needed