I just discovered this as well but I don’t think it’s a bug. Long story short, the Aeros doesn’t have headphone level out, I’m a bummed about that too.
The Aeros’s outs are not meant for headphones if I understand correctly, they are meant for a mixer or amp, so they have an “incompatible” impedance…er something like that. The BeatBuddy does have a proper headphone out though. So your guitar in coming into the Left channel at line level, and the stereo Aux Out is also line level – if you put a ton of gain using a boost/distortion pedal you will barely start to hear your guitar in the left headphone. The fact that you hear the click routing in both means that SS has a loud signal in both channels for the click.