Right. A USB cable has one HighSpeed line (480 Mb/s) and 4 separate SuperSpeed+ lines, each capable of up to 10 Gbps. USB 3.x uses two of the lines for USB 3.x transmit and receive (5 or 10 Gbps in each direction), leaving two lines for DisplayPort. If four lines are used for DisplayPort (HBR3 is 8.1 Gbps per line = 32.4 Gbps total on the wire = 25.92 Gbps of DisplayPort data) then only the HighSpeed line (480 Mb/s) can be used for USB.
Thunderbolt uses all 4 SuperSpeed+ lines at 10 Gbps each, two for transmit and two for receive for 20 Gbps total in each direction. Thunderbolt tunnels PCIe and DisplayPort through the same Thunderbolt connection. PCIe is used to communicate with a USB controller in the display. Any bandwidth not used by DisplayPort can be used by PCIe.
5K60 (936MHz) @ 12bpp = 11.23 Gbps. ≈8 Gbps for USB.
6K60 (1286MHz) @ 12bpp = 15.432 Gbps. ≈4 Gbps for USB.
Usually, a passive USB-C 10 Gbps cable can connect Thunderbolt at 20 Gbps. I'm not sure why a connection through a switch would cause a USB connection instead of allowing a Thunderbolt connection.
A Thunderbolt 3/4 cable capable of 40 Gbps can transmit 20 Gbps per line.