I'm doing a little googling and found one possible cause, at least for Safari. Open Safari's settings; switch to the Websites tab on top; then uncheck the box labeled "Share across devices". See if that helps, though quite frankly it shouldn't be necessary and wouldn't explain this happening with documents. It's checked here and I don't have this issue.
Another possibility I'm thinking is something in Accessibility (not sure offhand what it could be) or something like mouse or trackpad software. Do you have anything installed like Logitech's Options software, SteerMouse, USB OverDrive, etc?