Direct connection of UART serial port to USB type-C
From your last sentence it sounds like you actually want a working UART over USB. This will not work. The Rx/Tx pins in an USB-C connector has nothing at all to do with the UART in your microcontroller.

However, you will not physically damage the pins. USB doesn't use high voltage on the signal pins even if you use a high voltage for charging. This is even true for the initial USB.