Okay I'm posting this here, now, because I'm out of ideas and completely exasperated, plus a little out of pocket.
After changing my GPU (a simple swap, I'll get to this) from R9 Fury to a 5700XT, something changed in my system, and every time I used my microphone for anything it would simply blast a loud, pulsing static sound at whatever was listening.
I had immediately assumed that the cord connecting my headset, and its microphone, was broken; I was wrong. Replacement came and it's the same thing.
I have a video of my desktop, using Discord to listen-back, here: [[ Edited out as problem solved ]]
It's so infuriating because this problem is NOT:
the microphone, which I have changed
the cables connecting microphone, which I have changed
a problem relating to plugging the PC in to a ground, as I have checked
a problem with cables inside my PC coming unplugged, especially around the PSU - I just finished partially disassembling the PC and found nothing amiss since I put it all together in the first place
a problem with the 3.5mm jack port at the front - the back port exhibits the same behaviour
a problem relating somehow to the 5700XT - I did not need to install drivers or make any software changes to accomodate the swap. Just unplugged old, plugged in new, nothing else, and worse after putting the R9 Fury back in the problem still exists
I do have one useful tidbit that using a USB-based microphone, or a bluetooth microphone, works fine. So it's related to the audio network you connect the 3.5mm devices to.
Normal sound audio out is fine, nothing changed. As far as I can tell, nothing changed anywhere, my microphones all just sound terrible now for no apparent reason.
Pretty desperate for help.