Thanks for the update.
This definitely sounds like you are dealing with an issue with supporting Alt Mode or MST.
One thing to note about a KVM is it merely takes connections from an existing device and allows those connections to be switched to a different device. Docking stations like the UD-3900C4 utilize a single USB-C connection with the added support of Alt Mode and Power Delivery in order to break out all of those connections for the displays, multiple USB hubs, audio input, Ethernet and other connections that you have available on the dock.
I’m not aware of a KVM that will support a USB-C connection Alt mode or Power Delivery. There are full USB-C pass through switches that do exist, but they are very expensive and typically only found for industrial services.
Depending on which version of your Microsoft surface laptop you have, that may be able to support the full range of this stocking station. For example, we have tested and know that this docking station is fully supported by the Microsoft Surface laptop 3, 4, and 5.
I hope this information is helpful. And please let me know if you have any additional questions.