Nice one! Is this using the open core legacy patcher? Anything to note?
Big Sur and Monterey removed support for Legacy USB 1.0 peripherals. They work as long as they were plugged into the USB ports at boot time and never removed. If you remove them and replug them then they are not detected.
Workaround is to connected those peripherals to an external powered USB Hub. If you then removed and re-attached those peripherals from the USB Hub, then they work fine.
Try connecting your KVM switch to an external USB Hub.