A Limmited Slip Differential Question

Tanker said
I've only lived in this house since 2017 and the truck remains parked all winter. I've had to drive around another car to park up by the garage a total of three times, and each time it got stuck. Prior to that the truck was only driven on the streets of Los Angeles, so while burned up clutches as you describe may very well be causing the problem, I'd be surprised if it happened here in Pittsburgh. But this brings up another thought. The truck was rear ended while parked on the street in Burbank one night. It was hit hard enough that it was launched into the Mercedes parked in front of it, which was in turn launched into the SUV parked in front of it. Both of those vehicles were totaled. Could an impact like that have damaged the differential? The truck in question is posted below. And thanks to everyone that's offered advice. I appreciate the time you took to comment.
View attachment 1715902876

I understand. Here's the thing. The thing. The clutch limited slip units are made to slip when going around a turn, mainly. They are not really made to just let one tire spin. That's what kills them. It'll do it pretty quickly, too. Especially if it is the Track Lock. Now the Dana Power Lock would probably not slip to begin with in that situation, as they are a much more aggressive unit.