There is no firmware package available even in the AUR and seems to be only supported for fedora and rhel based distros so it’s your choice if you want to continue further or not:
https://bbs.archlinux.org/viewtopic.php?pid=1958713#p1958713
That firmware file has not been released yet even though the driver for that devices has been added to the kernel. That just means that the driver will fail and the device will simply not work (same as kernel 5.10 where no driver was available)
module: qat_4xxx, I didn`t find a firmware for it.