I am not sure how well you will be able to measure standby loss, unless you don’t use water for a long period. I have a heat pump water heater and it has sensors inside. Here is a plot of temperature and water usage:
You can see the last water usage was just before 1:30AM. The top and bottom sensors show the water is at 141-142 degrees. It takes a little over an hour to go down 1 degree (from 2:00AM to 3:40AM). It takes a little over an hour to down the next degree. At just before 5:00 things start changing dramatically. That is when the recirc pump starts (4:50AM according to IotaWatt, looks like I need to adjust the timer again, or work on a control system to control it better). You can see how the bottom of the tank has dropped 2 degrees in less than an hour, but the top of the tank is still the same.
Anyway, when I did another test many months ago, I discovered that measuring the heat loss of the tank was really hard even with two tanks and one bypassed. The water heater timers don’t really save much energy because the difference in heat loss of a few degrees is not so much. They probably save some by providing slightly less hot (temperature) water for the first usage in the morning. Now, the recirc pump is a huge energy waster. The pump itself uses very little energy, but the heat loss of a whole house’s worth of pipes (even when well insulated to R3) is quite large. But, having hot water without needing to wait is very nice.