I use version 1.10.1.1142 on windows 10. You can use (windows key) + Shift + (any arrow key) to switch applications between different monitors. When you use this method on full screen affinity designer UI turns non interactable. Shortcut's work but no mouse pointers register.
Correct me if I'm wrong but this problem precede this version and even other applications(affinity photo not sure on publisher) is affected. Short term solution:
Select designer and press (windows key) + down arrow, this will shrink the window and you can interact with it again, even turn it full screen and every thing works again.