I do not have clipboard sharing across my Win10 devices. I checked the link you sent and when I hit Windows Key + V to pull up the clipboard, I can see I don't even have it turned on (Honestly didn't even know about that feature). I also went to the clipboard page in settings and verified that nothing is enabled there either. On the Sync across devices section on my primary computer, it says "get started" and on my secondary machine it says "sign-in". As I'm not signed in to sync the clipboard, I'm under the assumption that it is not enabled.
I opened notepad and moved the mouse over it several times while having the Task Manager open and watched what was going on.
When I moved my mouse back and forth over a notepad window on the secondary computer:
The most noticeable thing was that the CPU usage for both Multiplicity and Notepad jumped. Where Multiplicity tends to sit around 1-2% while I'm controlling the secondary PC, when I move over notepad it jumps to 10-16%. Notepad went from 0% to 6% at the same time. Desktop Window Manager jumped from .7% to 3.5%, and System went from .8% to 2%. Those were the top 4 processes while I had the mouse slowed down by moving it back and forth over Notepad.
I didn't notice any significant jumps in the Memory column.
When I got it to slow down while over my desktop (no open windows) by moving my mouse around on the secondary computer:
Multiplicity jumped as it did when I was over the notepad app, but this time it was Windows Explorer that also jumped up from .3% to 7%.