Jeb,
If the cylinder is that worn, that is the most likely cause. If you look at pic 1 below, it shows the small switch that is likely either broken or it isn't opening the circuit when the key is removed.
I don't know if you need them, but I also attached the directions for removal and replacement. Additionally, the pass lock will need to be reprogrammed after you have the new key/lock cylinder.
There are two ways to do this. One takes ten minutes but requires a scan tool that can communicate with the vehicle's computers. The other way takes 30 minutes but doesn't require a scanner. I attached both at the end of the removal and replacement procedures.
I hope this helps. Let me know how things turn out for you or if you have other questions.
Take care,
Joe
See pics below.
Images (Click to make bigger)
Monday, November 15th, 2021 AT 8:54 PM