Correct. You can't just stream it from a characteristic. The only characteristic we expose is the one that allows to talk to the badges and request data. And you'll need to tell the badge to start recording that data.
I vaguely remember that in the example terminal there is a steaming command.
If you just want to use the badge as a "dumb" microphone, you will need to write a new firmware. In that case, you might want to use a nRF52 dev board that has a built in microphone. I remember seeing a few of these. The firmware should be fairly simple, since you don't need to deal with storing data and time sync