Sleep differs between SPI and UART. Sleep using UART is not a command but a control line/pin which can be asserted and de-asserted when using UART to communicate between ANT and your host MCU which is described in the "Interfacing with ANT General Purpose Chipsets and Modules" document. The Sleep pin in UART tells ANT it can turn off the serial port when it is unneeded thus saving power.
In SPI state transitions are generally automatic except for AP2's "Deep Sleep" which is also available on the UART.
However, AP2 does offer a "Deep Sleep" state designed for long durations between activity as it causes a full reset of the AP2, but in this mode AP2 will only draw ~0.5uA. That state is entered through a command specific to the AP2.
The Power Estimator can calculate the power draw for your use case and can be found
here.
I would recommend trying to mock up your system using an ANT USB Stick and ANTware II which has a full feature UI for ANT development.