The precise number reportedly was found in Tesla's papers related to importing the Model 3 LR AWD to Germany, according to reddit user Corio13, who found the image on German forum tff-forum.de:
According to the sources, the 2019 and 2020 model year cars were 79 kWh - so the new pack would be roughly 3 kWh or 3.8% more energy-dense.
That would explain how Tesla achieved increased EPA range ratings for the 2021 Model 3.
It would fit also with the previous news from Panasonic, who a few months ago announced upcoming improvements in the energy density at the cell level by about 5% in September and 20% total within about five years.
Several percent higher energy density plus some other improvements are probably the two main reasons behind the improved range in new Teslas.
Of course, the 82 kWh number is related to the Long Range versions of the Model 3 (not the Standard Range Plus). We assume that a similar increase will apply also to the Long Range Model Y.
Both the Model 3 and Model Y use 2170 cylindrical cells, produced at the Tesla Gigafactory in Nevada.
According to the latest news, the new cells will allow charging faster. It's something that yet has to be verified, but we might soon see an improved charging curve.