I've never seen a benchmark that shows a performance loss when connecting many displays or large displays.
The MacBook Pro 16-inch has a 5300M or 5500M (AMD Navi GPU) which supports Display Stream Compression (DSC) so 6K only requires a single DisplayPort connection using HBR2 link rate (like what 4K would use without DSC). You can connect a second display to the same Thunderbolt bus in this case if you like.
Considering the worst case, an older MacBook Pro that does not support DSC, the 6K display would require two HBR3 connections (only one such display per Thunderbolt bus). The second Thunderbolt port should be completely free for a Thunderbolt dock or storage device or USB device. I haven't seen a benchmark showing loss of performance from one Thunderbolt port when the other Thunderbolt port is doing dual 4K or single 6K. Actually, I tried it now on a MacMini 2018 with dual 4K from one port of a Thunderbolt bus and a Thunderbolt device connected to the other port and the device was able to receive 2600 MB/s which is near the limit of PCIe traffic over Thunderbolt.
A single Thunderbolt port has a max of 22 Gbps for PCIe traffic (2750 MB/s). I once tried raiding two Thunderbolt 3 ports but could only get 2800 MB/s which is considerably less than the 31.5 Gbps that you would expect from a PCIe 3.0 x4 device (3938 MB/s without overhead, typically 3500 MB/s).
PCIe bandwidth is shared between the two ports of a Thunderbolt bus. So if you're not using the USB of the XDR (5 Gbps) then the other port should have the full 22 Gbps remaining.
GPU and CPU temperatures may be higher which could cause slower performance? But that would be true for any display you connect.