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According to the manual, with Energy Saving on the start-up time is increased for the instrument panel, Bluetooth, data connection, and mobile app. I think it's because power to those systems is reduced or eliminated completely while the car is off, until you are ready to use it.
You might want to switch to percent battery rather than miles. This will give you a more accurate measure of vampire loss since it will not include a continually varying miles per charge estimate. Mine averages a little less than 1.5% per day.
On my 70D, my usual overnight battery loss is around 2 miles. Energy saving is always on. Climate is off and I always double click the Tesla app off. I do not check it the battery everyday. And, on occasion the screens will be dark when I open up the car after it has been sitting for some days but only takes a short while for everything to come back to life.
Our pre-autopilot car that had just received a firmware update the morning we drove it to the airport sat in the parking garage at Phoenix Sky Harbor for 9 days and used 28 miles of range - it was very hot in Phoenix while we were gone, but the car was in energy savings mode and we never checked on it prior to our turning the AC on about 2 min before we got to the car- It was probably in a pretty deep sleep. In our case vampire losses of 3 or so miles per day are normal. Not anything to worry about as far as I can tell