To clarify, websites can’t capture keyboard events that were typed into a different website like you’re thinking. Think of going to a web game that let’s you use WASD for controlling your character. It’s able to capture those events on that page because its in focus. When a site goes out of focus (such as switching tabs or switching to another window that’s not the browser), it loses that ability. Overall, it’s very secure.
I was more wondering how you thought capturing the mouse movements would lead to security issues.