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Any indication of the 82kWh pack?

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There are two threads kicking around on this. Basically, there's good evidence that at least the MYP was getting the 82 kwh pack as of the 2021 model change. Owners have approximated it with charging information and Tesla's own EPA submission shows the MYP as taking roughly 82 kwh of charge and the MYP as taking roughly 75 (IIRC) kwh of charge.
We got our new MYLR down to about 15% and charged it back up, and it extrapolated into the mid-70's kWh. So my guess is the LR doesn't have it, or if it does it's expressing a range in terms of the older battery capacity.
Figure out how many estimated miles remain of the original 100% estimate, calculate how many kWh were needed to reach 100% again, and extrapolate. If you were at 10% and took 67.5 kWh to reach 100%, then your battery would be 67.5 * (100/(100-90)) == 75 kWh.
It is not clear to me exactly what you were saying here, but it is not a good idea to trust what is reported on the charging screen, because that does not reflect what was added to the battery.
That is just a simple calculation of your vehicle constant * miles added. In reality due to vagaries of how things are displayed, the actual energy added to the pack is typically considerably less (by a few %).

It is easier to use the trip meter to calculate energy between 0 and 100% (with correction for heat loss), and then correct for the buffer size.