What might be causing periodic audio pops and crackles in certain Windows 10 applications?

After nearly 18 months of accepting persistent audio crackling issues as the norm, I found the culprit earlier this evening.

Corsair's iCue peripheral management software

I committed to a clean install of Windows 11, using the upgrade as an opportunity to track down the source of audio issue once and for all. It was only after I installed this software that the issues start, verified with a revert via a Windows system restore point.

Here is another report of this issue: https://forum.corsair.com/forums/topic/168593-icue-causes-audio-stuttering/

The software has been updated several times in the past 18 months and I therefore have no confidence that the issue will be fixed. Ironically, I was using the software only to turn off the bright DPI-indicating LED on my mouse, a feature I can live with given the alternative.