The USB-C port uses USB 3.2 Gen 1 (USB 3.0) and therefore has a maximum bandwidth of 5 Gbps. Pretty much any USB-C cable should work as long as it is USB 3.
Unfortunately, 240 Hz will not be possible, at least not in 4K. According to the instructions from Asus, a maximum of 4K@144Hz is supported via USB-C when DSC is active.
EN:
https://dlcdnets.asus.com/pub...> "Type-C bandwidth: Select USB Type-C with USB 2.0 or USB 3.2. USB 3.2 is up to 3840 x 2160@144Hz when DSC support is switched ON."
EN:
https://dlcdnets.asus.com/pub...> "Type-C Bandwidth: Select USB Type-C with USB 2.0 or USB 3.2. USB 3.2 is up to 3840 x 2160@144Hz when DSC support is ON."