Yes, I agree, so the next question is what am I looking for inside the soundbar to determine if this is the case?
These usually have separate sections, sometimes even on different PCBs: one is the power supply and battery charging unit, another one is the audio amplifier circuit, and in this case a third one is the bluetooth part.
Do you have an oscilloscope (even a cheap $30-$40 one)? Measuring the output of the supply circuit for ripple and noise within the audio frequency range (say 20 Hz to 20 kHz), when on battery power and when powered from USB, would be my suggestion. Short the audio input to ground, for example making a custom plug or cable with left and right shorted to ground, so only the inherent noise of the amplifier is visible.
On the audio amplifier side, you should be able to identify the audio opamp(s) used, and determine the power rails from those. It will very likely use a single-sided supply, i.e. VDD at some positive supply rail, likely 5V, and VSS at 0V/GND. Then, the input audio will be biased to somewhere around 1.8V or 2V or so (line audio is about ±1V, and the DC component will be rejected on input using a capacitor), and exactly how it is done matters a lot: a resistor divider between the supply and ground is most likely, and the noisiest, since supply rail noise is output only halved. Analog
AN-581 from 2002 describes better voltage biasing schemes, and they are simple enough to be bodged in if you can reverse-engineer the amplifier part.
I'm just a hobbyist, but I did try to find its schematics or pictures of its (MF8395) PCB(s) to see what specifically to investigate, but couldn't find any. I'm pretty sure its schematics and repair manuals and such are out there somewhere..
They aren't both connected to the same soundbar.
Ah, apologies; my mistake.
when I plug in the PC soundbar and my LCD TV is on (same wall outlet as the Mega Drive), the TV doesn't lose sync, only the PC monitor does.
To clarify, the sound bar is not connected to the PC monitor at all, just sits beneath it?
That sort of glitching does usually indicate a ground loop or at least a bounce or spike in the PC monitor signal ground. It could also happen due to sudden change in surrounding magnetic fields, and speakers are basically just huge coils, so it could be just due to the magnetic fields when the speakers are first energized; I dunno.
what should I be looking for to discover where this apparent electrical noise is coming from when the soundbar is plugged in but doesn't make noise when it's on battery only?
With input shorted to ground, one would need to track the audio signal to see where noise appears when running from USB, and disappears when running on battery only.
My bet is on it using single-sided supply and a voltage bias for the amplifier IC(s) that passes half the supply noise to the output audio; see the above AN-581.
The question is, since this is a design issue and not a fault, are you willing to risk the unit to hack the noise away?
Or, would you rather first set up a low-noise 5V USB supply, for example from a lab power supply, optionally at 7-8V and linearly regulated to 5V (needs a heatsink!) at over 2A current, to see if a true low-noise USB supply gets rid of the noise?