So far, I have not come across such an "Auto Standby" function.
I operate the device on my 12V connection on the console (vulgo cigarette lighter socket) inside the vehicle (Mercedes-Benz B180, JG 2011), which is conveniently switched off at the same time as the ignition is switched off.
This way, the problem of battery discharge does not arise in the first place.
Otherwise, take the 12V power supply for the Albrecht DR57 from the switched power supply of the ignition lock.