Your USB-C connection is fine. The USB connector in the handset actually connects inside the handset to a USB to serial converter, made by Prolific.
The problem probably is that you don't have a driver installed for it. To fix that, you can download a driver for its PL2303 chipset.
For example, from this link:
https://www.prolific.com.tw/US/ShowP...id=225&pcid=41
Regards, Andrew