As far as I am aware, the recent Logitech headsets are all digital and use Avnera devices
https://www.avnera.com/ As its digital, interference can degrade the signal, but its extremely unlikely you'll 'hear' the actual interference, but rather its effect on the error correction and channel coding of the link. So any hisses and tones you hear wont' be the actual RF interference.
I suspect significantly less bandwidth is given for the mic than the stereo audio because for 'voice comms' it is still generally thought that 'telephone quality' is acceptable. Whilst the quality of the voice channel in modern wireless headsets is great, it probably means that there isn't much in the way of error correction or error masking. Given the choice between complete drop out - at the limits of its range, or from interference - or a reduction in quality, for voice comms you generally accept that it won't always be crystal clear and that its more important to 'hear the voice' than to 'hear the voice with crystal clarity - its not meant for hifi digital recording. But for the speakers/headphones, the downstream where you listen to music, games etc.. because its providing sound to you, any noise/glitches are very noticeable so this gets more attention, and much more bandwidth to prevent a horrible experience.
Having been almost obsessed with wireless audio for many years (making wireless headphones, wireless guitar, bluetooth headphones etc..) it is only in the past few years that devices have come out that can carry high quality audio, with low latency, with few artifacts. Sure they can avoid fixed band interference most of the time with adaptive frequency hopping (black listing channels where packets dont' get through) but how they cope with strong interference across many bands is tricky, and there are measures taken such as forward error correction and 'error concealment' which cannot guarantee a clear signal, or no artifacts, but do a fairly good job of making them less noticeable.
If that noise has only just appeared after many months of usage then it could well be a failing component. If it has always been there (on occasion) then it could be anything from crowded spectrum, multipath fading (even at a range of a few feet there will be 'dead spots' where the signal quality dives) or a consequence of the algorithm used by the link.
I would send a known signal, like a 1kHz sine wave down the mic, and record the result for 10 minutes. Then look at its spectrum to see if there is simple wide band noise, or very specific tones. Sounds like it'll be an arse to track down, especially if its interference based.