Unfortunately current CYBT-213043-MESH board have some leakage current; Because of which it can't be powered by coin cell battery.
There are current leakage to USB chip, it make CYBT-213043 module can not work in power battery supply.
But if you are developing a custom board for end application, it should work with battery supply.
If you want to evaluate CYBT-213043-MESH kit with coin cell , then you may have to try as below:
Hard cutoff HCI_UART through SW4 and cutoff PUART through FW, it will prevent current leakage. After that, CYBT213043 module can work in Battery supply.