Split Dongle

With split keyboards, there needs to be a "central" that maintains state across the keyboard halves and keeps the two synchronized. Ideally one would use an external USB dongle for such purpose as that ensures the longest battery life for the keyboard halves. In such a setup, the dongle central would receive keyboard data from the keyboard halves "peripherals". The central subsequently acts as a unified keyboard to the computer that it is connected to via USB and additional device that it's connected to via Bluetooth.

This is very efficient because the peripherals only need to send data. It can rely on "interrupts" to detect and wake when a key is pressed but sleep whenever it is not in use. A 400mAh battery would last around a year.

The dongle central must be constantly awake and ready to receive data from the peripherals. The dongle's power consumption is less of a concern because it's either plugged into a computer (for use over both USB and Bluetooth), a power brick (for use over Bluetooth), or portable charger that has significant capacity (for use over Bluetooth).

Without a dongle, one of your keyboard halves (typically the left) must act as the central half. It would use a lot more power and would last around a month on a 400mAh battery. The other half (typically the right) remains a peripheral and would still last around a year per charge.