How does the mesh network handle deep sleep, anyway? Do they synchronize clocks so they all wake up at the same time, or does a node just transmit continuously until someone reasons?
To send data to a node in sampled listening mode, the sender sends a string of smaller wake-up packets that indicate when the sender intends to send the real data packet. When the receiver picks up the wake-up packet, it knows when it should wake up again to receive the data packet, so it can safely go back to sleep again for a while. And if the sender knows that the receiver is in always-on mode, because it is powered by a wall-socket, the sender can skip sending those wake-up packets, saving a bit of power.
This requires clocks to be synchronized, but only loosely - millisecond synchronization is enough. The trick is to strike the right balance between communication responsiveness and power consumption.