It happens only on the server side. Both client and server are i7 9700K (which does not have hyperthreading while your i9-9900k does... might be a factor) with Logitech mouse and Corsair keyboard. G Hub and iCUE are both installed and I tried turning both down to minimum polling with no effect. I also tried closing both of those completely with no effect.
There is no trigger and it behaves this way from startup to shutdown. I have only tested seamless mode, not KVM.
I have been investigating further and cannot get a i9-9900k to show anything remotely similar.
All cpu cores are happily dropping to 800Mhz when nothing is going on. There are occasional spikes to upto 4.7Ghz across all cpu cores, but that happens with or without MP running when moving the mouse between apps (as each app no doubt processes mouse move messages)
This was using OpenHardwareMonitor.
What does that tool show for you?
I will say that gaming mice tend to send an absurd number of mouse move messages which will inherently use way more cpu (and network bandwidth), but this would only be when actually controlling another computer.
Ryzen processors may be different as they are sensitive in different ways, but an Intel i7 and i9 using the same socket and generation of cpu core should respond the same so that implies there is another factor here as well. Either a monitoring tool difference between us or some other bit of software also involved.
If you do not move your mouse at all, what cpu behaviour are you seeing?
Also are you using audio sharing? When that is connected the OS periodic timers will be running at a higher rate. This is needed because audio sharing runs very small buffers so response time is critical.