The device could offer multiple options for the audio played when it is connected.
There is the current connection message. Some people would be fine with what the device is currently doing.
When you connect the Bragi headphones to a device, it can announce which device it is connected to. (e.g. “Connected to Samsung Galaxy 7”, “Connected to Desktop”, etc…). In the presence of multiple audio devices this could take the guess work out of which device connected when you turn on the Bragi Pro headphones.
The device could just play a special tone when connected. The advantage here is that if your audio source is already playing the connection message overlaps with less of the audio source.