Over time, and hard shifting damage to the gears in the differential of my Chevy Tahoe?
It depends on how hard.
Can you provide more detail on what you’re dealing with?
I doubt it. I learned to drive with a rear drive car and relentlessly abused my dad’s car when I drove without him around. I saw a lot of what some others did to abuse their cars including drag racing and speedshifting manual transmissions. Driveshaft universal joints were the first thing to fail with driver abuse and fortunately they gave a recogizable warning noise when in the process of failing. Rear drive/differential gear and axle failures were extremely rare.
How old is the Tahoe, how many miles on it? Are you using it as a tow vehicle? Has the differential fluid ever been changed? For hard shifting to damage a differential it would have to be shifting so hard so often you likely would not have put with it and had the transmission problem addressed.