Quite possible transport is encrypted, but that can likely be overcome with some RE on the Android app. Given the price of this piece of hardware, it's likely recoverable with moderate effort. At least worth a try.
yeah, my point is "1 night and $20 of Claude token" maybe not enough.
Also you dont really need the nrf52840 dongle if you want sniffing(Also unlikely to work after the pairing process is done), you can use btsnoop on Android phone to record data, then analyze it with wireshark.