It seems to be a consensus from everyone who posted here, that, rather than damage, there is "something" causing noise. I have already ruled out the phone, and also plugged the speakers into a different device, whereas the noise wasn't present.
First I checked the connection, and there seems to be an infinitesimal movement when the jack is fully plugged in (a standard audio jack). When I try to move it around it does crunch a bit, but it is nothing that would resemble the noise I experience.
I opened the pc, and cleaned the audio "area" on the motherboard. I went at it with a magnifying glass. No caps were blown, no visual damage present.
But I did notice something. Back in the day, ASUS did brag about having top notch noise insulation, so I went inspecting that. Its a thick line that separates the audio area from the rest of the motherboard. It looks like gold, but the color pulls a bit towards yellow. Upon closer inspection, that insulation looks cracked up, like leaving mud in the sun for long that it dries up and cracks.
I check the closest objects to the insulation, and these appear to be managing the M.2 I have installed. I suspected there being a correlation between the noise and storage activity. A light bulb went off!
I ran a live distro on a USB stick, upon which I watched a couple of youtube videos. No noise. Then I mounted my secondary hard drive and tried a few movies on that one. Again, no noise. And then I mounted the M.2. At first, no noise, but as soon as I started watching a video from it - NOISE! The exact same occasional bursts that have been happening before.
My M.2 being active is causing this. Probably a coil or cap charging or discharging, and because the dampening is shot, it translates as noise into the speakers. DAMN!
So how do I fix it? Heat gun?