It's what's called EMI (electromagnetic interference).

Let me give you an ELI5 rundown of what's technically happening here:

You have two types of signals: digital or analog. An analog signal is much like a real sound wave, think of that bouncy and pointy visualization of music that you see on a TV commercial. I'll call this a wave. A digital signal is more boring. To oversimply a digital signal, a very basic digital signal basically has two states - a 1 or a 0. Think of a camel's back. You either have the normal back (a zero) or the hump (a one). It's very hard to mistake one for the other.

For practical purposes, all consumer grade audio equipment eventually converts over to an analog signal. That is just required for playback on something like speakers or headphones. But all digital sources (spotify, a music file, a video game) exists in a digital signal. Eventually that digital signal arrives at what is called a DAC (digital-to-analogue converter).

When a signal transmits digitally, it's easy to tell if it's the camel's back or the hump. Its still prone to EMI (electromagnetic interference), but because a zero and a one are magnitudes greater than each other.. the device can estimate "this is a camels back, this is a hump, done, done, done reconstructed - OK now let's convert to analog." With analog signals, or that wave, it's a lot harder to reduce the EMI noise (there are ways to do it such as a separate cable measuring just the noise - but this isn't exactly a setup you see with most consumer grade equipment).

So DAC (digital-to-analogue converters) are the way we convert a digital signal to analogue. Everything needs one. Your 1990's Gameboy has a DAC, your blutooth headphones have a DAC (wireless signal is sent digitally, they convert it to analog), your motherboards soundcard has a DAC, etc., If EMI is a problem, the goal can either be to reduce EMI, shield things from EMI, or preserve the digital signal as long as you can to get it as far away from EMI sources as possible (basically, use a USB device that's a DAC to push it down the foodchain). Motherboards and soundcards sometimes come with good EMI shielding, but it can be sketch especially if there's a grounding issue in the case.

EMI comes from a lot of things. Your computer case is an absolutely massive source of it. Bad wiring in the walls can be a source of it. Any USB device like your mouse uses electricity to communicate with the motherboard.

So with that all out of the way what troubleshooting steps would I take here? Isolate all of your analog audio cables and run them in ways where they do not intersect with any other cable. What's likely happening is that your mouse cord and speaker wire OR motherboard audio output are "crossing." When you move your mouse, an EMI signal is sent through the USB cable and a speaker wire overlapping and that speaker wire is picking up the EMI signal from the mouse. This is extremely common.

A lot of desks have cable management holes which are great for digital signals. As I explained: yes interference is happening here, but it's rarely enough to confuse a camels hump with the camels back. If you run your analog audio cables through that same hole, you'll likely have degraded audio quality.

One fix can sometimes be a standalone DAC. This is a little box with a USB cable that basically takes over the role of your motherboards soundcard (you're now bypassing it and a USB device becomes much like the soundcard). The downside of standalone DACs is that they're typically intended for headphones or 2.0 setups. For 5.0/5.1/7.0/7.1 your DAC is often either a home theater box or a quality motherboard with EMI shielding (make sure those cables don't cross or run them through something with more EMI shielding).

I don't know your exact config, the pipeline, and where things are in the food chain - but I'd bet you being strategic in running any analog audio cabling it may solve it. If you don't add a DAC in an EMI safe part of the pipeline, you'll probably still have some EMI interference on your analog signals.. but you can usually get it sounding 'good enough' without it.

Sorry if I explained that bad or there are typos. I did a quick writeup and didn't proofread it. If anything doesn't make sense, I can attempt to explain it better.