Razer keyboard vs. KVM switch, connectivity issus

I am using a newly bought DeathStalker V2 (wired keyboard) and a KVM switch to operate my home, Windows 10 PC, and a Windows 11 work PC. Both PCs run the newest version of Razer Synapse 4.

When switching from one PC to the other, the keyboard seemingly loses power, does not register keypresses, no lighting. When I switch back to the original PC, it again works. If, however, I reconnect the USB cable on the second PC, it now works there (popping up as a device in Razer Synapse), but ceases working on the original PC in the above fashion (and is not anymore listed as a device in Razer Synapse there).
When I switch from one PC to the other, but that one is off, the keyboard loses power, but when switching back, it again works.

Please note, that with this KVM switch, other keyboards, such as a Logitech G815, a Cherry Stream, and a big number of other USB devices, such as mice (including two different Razer models), webcams, USB sticks all work as expected.

I as assuming a general flaw in Razer USB power handling either in hardware or in Razer Synapse.
Can anyone confirm this, or knows a workaround?

It would be a pity to have to return this otherwise fine keyboard.