I also had a buzz in the left channel. As you said, it's most obvious in the few seconds after pausing, as there's nothing to cover it up, but I suppose the bluetooth board has yet to stop sending output to the amp. Last year, when troubleshooting, I recorded some silence on an iPad to play back in the car, so I could turn up the volume and record the result with my phone while driving.
BlueSaab_left_speaker_buzzing_1.m4aHere is one of those recordings. Is this the same sort of buzzing you have?
For me the noise would show up for a few days at a time, then stop for days. It was directly related to engine speed. Ultimately I believe the noise originated from my alternator with a failing voltage regulator. A few months ago it failed completely and I replaced the entire alternator (A miserable job on the 9-3). Since then I haven't heard the buzzing.
I did also freshen up the ground wire from the wiring harness to the stud in the corner of the trunk, along with some DeOxit. I do think that helped, but with the intermittent nature of the problem I'm not certain.
It's interesting that this interference only makes it to the speakers on one channel from the BlueSaab, without affecting the other channel, or any of the other audio inputs for the stereo. I wonder if some filtering on the power or ground inputs to the BlueSaab would kill the noise, but I guess it's better to cure the noise at the source if possible.
2001 9-3 base