I would look at the man page for lsmod; to my unexperienced eye it sounds like the kernel module containing the driver is not loaded. I am guessing that is what UNCLAIMED refers to; no kernel driver is claiming this PCIe device as its responsibility.
Missing firmware is usually an error visible in dmesg, and it is an error message from the appropriate kernel driver/module in effect saying, “I am here, I found the device I am responsible for, but I have no firmware to give it”; this appears to be more like a situation in which lshw is saying, in effect, “I found a Mediatek device, and my PCI ID database says it is a Network Controller, but nothing in the kernel knows what to do with it.”
Edit: this device was completely missing from the PCI ID database, therefore that is not where it was identified as a “Network Controller”.