Even if it looks and smells like new gear oil, there is probably a large amount of wear metal at the bottom of the housing.
Almost nobody changes gear oil unless some repair has been made in that area.
I suggest removing the differential pan, blasting everything clean with brake cleaner, then reinstalling the pan and refill.
Know the viscosity of oil that is specified, and if it has a limited slip differential. If there is a limited slip differential, either buy oil that already has the LS additives, or buy oil and additives separately.
I am guessing that this vehicle takes 75w140 syn. Valvoline and M1 are easy to find, sell at a low price, and already have LS additives.