Known as TypeC's "alternate mode" (Alt Mode). Most of the devices that can output video through the C port are done through DP Alt Mode. In this mode, the DP signal can choose to occupy half or all of the 8 lanes. Because the display signal has only one direction, every 2 signal lines form a DP channel.
DP1.2 up to 5.4Gbps per channel, DP1.3 up to 8.1Gbps per channel. The bandwidth requirement of 4K60 frame is 12.54Gbps. So for DP1.2 equipment, 4K60 needs to occupy all 8 lanes. (In fact, 6 are enough, but DP does not have a 3-channel configuration, and USB3 does not have a half-duplex mode.) USB can only use the old USB2.0 channel. For devices with DP1.3 and above, only half of them can be used, leaving the other half for high-speed USB in single-channel mode.
So the answer is, it depends on what DP version your monitor and computer or adapter supports. If both sides support DP1.3 or above, it is possible to retain the high-speed USB interface while maintaining 4K60. If you only have DP1.2, you can only choose one of 4K60+USB 2.0 and 4K30+USB3.0.