Most water tanks should have a thermostat, that is normal. Since you need to set a safe water temperature for the tank. Imagine if you put the hot water schedule on 24/7. If the water thank did not have a thermostat on it it would keep heating the water until it malfunctioned. That is why you my notice even if you have the water tank scheduled to be on all that that it is off, as the water temperature set on the thermostat on the tank is achieved and it deactivates the tank.
That is why there is no hot water history, as you could have the water scheduled to be on 24/7 but in reality the tank will turn itself off when the temperature on it is achieved and only turn back on one the temperature drops or hot water is used and fresh water fills the tank back up, cooling it down.
Let us try something next. Select the hot water control in the Nest app and tap in the upper right corner to go into settings. There make sure to toggle the first option you see there to off. This will disable the hot water schedule. We want to turn it off, just to check for a day, and see if this activation behaviour still happens with the schedule off. You can still boost the hot water should you wish to activate the tank to heat water.
Just keep an eye on it for a day and see if it still activates with the schedule off. If you do notice activating like before have a look on the display for any water drop marks and note if the heating is off or on at that moment.
