Car Information: 2006 Jaguar XJ8 4.2L ~135,000 miles

I was shoveling around the car after a snow storm, I reversed the car into a shoveled region of the driveway to finish shoveling around where the car was. When I was finished, I attempted to get to my original position, however, due to the driveway being somewhat slick and the tires couldn't get much traction. I was able to change gears no problem and had to put in park to try to melt the snow/ice around the tires multiple times (drive -> reverse -> drive -> reverse -> park). However, after the 3-4th time (finally put salt around the tires and where I needed to go), I started the car, let it warm up, and try to drive up the driveway again. Once again, I could get back up, so I put it in park, lay the rest of the salt down, and was going to try again (car is still on). However, I could not get the car out of park. The gear selector stick is not stuck in park, I am able to move it freely throughout all of the gears, but the car seems to think it's in park. The break lights work, I just put in a brand new battery, the car had major repairs on the rear suspension crossmember before the snow storm. No indicators came up on the dashboard came up besides one saying it couldn't engage the parking break. What could be the cause of this issue, and how would I go about to fix it? I scoured the internet trying to find something similar, but I couldn't find anyone having issues besides the gear selector stick physically being stuck in park. I've asked chat-gpt for potential causes and it came up with the gear selector itself, saying that it was bad and needed to be replaced. If anyone had any thoughts, please let me know. Thank you!

 

TSBs for the X350 but might not be in the VIN range?

 

Check shifter bolts on transmission.