Good news, everyone! There exists a predefined quirk in the linux kernel that we can as of version 5.15 apply to our laptops that will automatically manage the muting and unmuting of the LFE properly. For older kernel versions you'll have to use the old solution below (or patch and build the kernel driver yourself). We just have to create/edit the following files:
/lib/firmware/hda-jack-retask.fw
/etc/modprobe.d/hda-jack-retask.conf
first off the hda-jack-retask.fw file should contain the following: