So, this is really random, but if you can open up the case and figure out what is whining, folding up tinfoil neatly in half about a dozen times will make a really effective shield and cut like 95% of the whine. I found out about this trick from an open-source synth (PreenFM 2, incredible little frequency modulation synth) that had some whine due to the display. Sticking the thick piece of tinfoil between the display and the PCB boosted the SNR an almost unbelievable amount. Give it a shot, it only costs time and tinfoil! Be sure to stick some electrical tape around anything it might contact though, so you don't short anything out.
I've had my ts3 for a couple years now. I just noticed a pretty bad coil whine on mine lately. I'm not sure if it's always been there and my environment's changed or the device just suddenly started making the noise.
That sounds like exactly the issue I've just described when I plug a USB C display into mine. I actually notice it, albeit to a much lesser degree, when I move a USB mouse connected to the dock.
I've tested 5+ TS3 Plus docks, and all of them have a coil whine, which can be heard in a quiet room, without playing any music.
Sometimes I like to work in silence, and the coil whine really bothers me.