So I've exhausted the resources online but maybe someone knows some more info.
The microphone array on the X1 Carbon's from the 6th/7th/8th gen on have a 4 channel microphone array at the top. I recently reinstalled 20.04 (with kernel 5.8.0-45) and only the two microphones on the left side are registering. I've had the same issue with 20.10, kernel doesn't seem to matter (5.4, 5.8, or 5.10). What I've noticed, however, is that the live instance of Ubuntu does not have this issue and both pairs (left and right) of microphones are registered and pick up sound.
The issue: Once everything is updated after installation, the right side mic is disabled - so some update is breaking this - but I'm not sure which. One weird fix is to change the CapturePCM "hw:${CardId},6"
to "hw:${CardId},7"
in the file /usr/share/alsa/ucm2/sof-hda-dsp/HiFi.conf
but this breaks the control on the mic as the mic control will only control the left two mics. However the live-boot instance has this value set at "6" so it shouldn't be the final fix.
If you have a X1 Carbon 6th, 7th, or 8th gen (maybe 9th as well?), check if the microphones at the top right of your display appear to register any input levels in the Sound tab in Settings when rubbing your fingers over them.