Hello @EKTan
Note: I don't own a BTC Base so my conclusions could be incorrect.
that said, the BTC Base is mainly for M5Stack (Base and Gray) which include the Battery Bottom. So mechanically you'll need at least a Battery Bottom stacked to the M5Core2 to make it work with the BTC Base.
Note: in order to be able to stack the Battery Bottom to the M5Core2 you'll have to remove the small board (which contains the IMU and the microphone) as well as the bottom already installed on the M5Core2. By doing so you'll lose the IMU and the microphone.
Note: the Battery Bottom only is available in gray or black.
Thanks
Felix