>site using JavaScript to time how long it takes you to hit each individual key press and how many times you hit backspace

You mean like a video game? Are video games now nefarious applications tracking you? Your browser is not "leaking" anything to websites. It's hard to understand what you are even complaining about. If you don't want grammarly to record your keystrokes, then don't install grammarly.

It's like ordering a beer and then complaining about alcohol.