Okay, so, my pal came over. He thought it might be a driver issue so we plugged my (wired) headset into the laptop to see if it updated. It didn't update.. but at the same time, he plugged his headset into he usb at the back of the ps5.
We didn't change any settings, and didn't do anything else, but, for now, it seems to have jumpstarted the system to recognise my headset.
I don't know if any of this helps, but if you have another headset, or a close (proximity) friend that can plug theirs into yours, it might just work. I'll post again if it drops off.