Are you sure you don’t mean T2U?
The inxi doesn’t show any wifi cards only ethernet - if it is T2U it is connected using USB and lspci will not list the card - use lsusb instead
lsusb
I have a couple of those TP-LINK Archer T2U and in my experience it does not work OOB.
I built a custom package for it - let me see if I can dig it up.
Using the provided output - specifically the device id - I did some searching - I was mistaken - the device is a pci device and seems to require special attention to get working with Linux kernel.
From a topic on AskUbuntu
It seems possible using sources from something called rtw89 which can be custom-built from AUR
As this is a dkms package - you must install the kernel headers for your active kernel as part of the process to get it running.