logitech unifying software mac not detecting
The system information is showing that the hardware is not being detected. The drivers are probably fine but idle since they don’t see the USB hardware for Logitech. 

You can confirm this by removing logitech, then plugging in another usb mouse or something and refreshing the System Information. You should see that device be listed and know your Mac and USB are fine. 

Once you’re sure the Logitech dongle is not working, here is a DIY repair you could try if you can’t get a repair / replacement part:

The fix is to remove the black cover, remove the chip, insert a piece of paper that raises the metal connectors of the chip closer to your laptop's USB connector. Reassemble everything. Once the chip and the USB port are properly touching again you will see the receiver show up in the Mac Systems USB panel and in Logitech Control Center, as others pointed out. You can also look for a visual tutorial of this on youtube / google.

As these age, this is, sadly, a widespread problem with the Logitech receiver.