Does this only happen if you use your speakers, or does it also happen when you use headphones?

There are ways for speakers to get annoying interference, like a 60Hz buzz in case if a ground loop. It’s also possible that long wires will start acting like antennae, to the point where a wire of the right length can actually become a shitty AM radio receiver by accident. Any wireless electronics in the area, or other insufficiently isolated electronics, can end up sending radio waves that an antenna like a wire may pick up. Better speaker wire (with more insulation) should help prevent that issue. Adjusting the wire’s position may also help.

If you use short headphones and the sound issue remains, there’s a chance the problem lies within your Deck. There could be a design flaw or a defect making the Deck interfere with itself. There isn’t much you can do in that case. I suppose you could get a USB dock with a digital audio interface on it to move the audio circuitry outside the Deck, that may help.

Also worth checking is if the problem disappears when you disconnect the charger/dock. If you’re dealing with a ground loop issue, the interference should disappear or at least get a lot better as soon as you disconnect the Deck. For ground loops you can try making sure you plug all devices into the same circuit/socket, or adding a ground loop isolator between the Deck and the speakers. Getting better audio cables will also reduce the problem, but it won’t disappear completely. If you’re not using a good charger (i.e. a shitty charger that came with a cheap USB dock), you can also run into problems like these.

I’ve also heard a similar problem on an old device of mine that had to do with the sound output being switched off entirely if it hadn’t been playing sound for a while. The workaround was to prevent the system from turning off the audio hardware, but I have no idea if that’s even something the Deck does at all. You could try playing an endless loop of empty audio in the background to keep the sound system active if that’s the problem you’re facing, but I kind of doubt it.

Because you describe the problem as something that only happens during certain computationally intense activities (staring a game, changing settings) I think interference from inside the Deck is the most likely problem. However, a ground loop issue can also be made worse by changes in power consumption of the device, so that’s also a possibility at the very least.