The real SOC doesnt drop if the battery cools down, only the displayed SOC.
This is a active choice from Tesla, as the SOC measured still is the same when the battery cools.
Any big difference in displayed SOC only happens if its very cold outside, like well below freezing.
The high voltage battery itself is very safe at low SOC. No need to worry about that.
We only need to make sure that the high voltage battery dokt get completely discharged (thats well below 0% on the screen), as this means the low voltage battery does not get charged from the high voltage battery which it need to be about daily. If it do not get charged, the car ends up not possible to wake up and probably need a new low voltage (12V) battery. (If you have a 16V lithium batt it needs to be charged.)
I often leave my car at lower SOC, working weeks means arriving at ~ 10-20% SOC and the car stays there or I do some short drives to the store, so it stay around 10-15% mostly during these weeks.
My M3P ’21 had minimal degradation after 2.5 years / 66K km.
It had not ended up as the M3P on teslafi charts with the lowest degradation if low SOC had been bad. (It’s well known from science/research that low SOC is not bad at all, so the conclusion do not cone from my car only).