In the keyboard they are in series. Maybe in the mouse , in parallel , maybe not. They both go to the same USB receiver which has no battery.
My only thought to try to think of something even possible is that the interface between the two batteries provides enough resistance such that the extremely low current draw doesn't happen across that interface but only where the battery that dies touches the Nickel or whatever coated contact. The fact that current flows until one battery is totally dead says that in doesn't need the 3+ volts between the two batteries but just the 1.5 or less between the two ends of the dying battery. Maybe the keyboard just needs some potential difference (could be just 1.5 volts) to work.
Volt meters , for example have a theoretically infinite resistance (and therefore theoretically no current flow) but still sense the potential difference between two ends. Now suppose the keyboard circuit just needs some minimum voltage to operate and the current draw is super super small. The 1.6 volts between the two ends of the battery that eventually dies provides enough driving force to push that tiny current. As it does , its voltage drops until the voltage sensed between the ends of the two batteries in series drops below say 2 volts (1.6 in one and .4 in the dying battery). Maybe when the keboard circuit senses less than the suggested 2 volts total ( 2 being just an example) , it shuts down.
So anyway , the idea is that the resistance between the P and N ends of the batteries where they touch in the center is high compared to where the dying battery touches the Ni plated contacts at its end. The current all flows do to the 1.6 or less voltage in the one battery but the keyboard senses the 3 volts even though no current is flowing between the two batteries , just like the volt meter senses the 3 volts between them in series even though it has the theoretically infinite resistance so no current flows through it.
Now of course there is no infinite resistance and so there must be some electrons flowing to allow the keyboard to sense the 3 volts but that amount is almost nothing compared to what flows out of the single battery just driven by the 1.6 volts because the resistance on that end is lower.
Make sense?......
Now let me tell you about the Tooth Fairy.
