I think you don't fully understand. They aren't just doing a search based on the key being pressed down. They already did a search based on the previous characters that returned results for all possible next characters. So by the time you type a second character it just checks results locally from the search that had likely already been returned from when you had typed the previous character.
They do that, yet proceed to kneecap the perceived latency by delaying the render.
> And on keyUp (the user releases the key), we render the suggestions.
There are a large number of edge cases where rendering it on key down would not be desirable (user types Ctrl+v, how accented characters are enetered, how some Asian languages get handled, backspace/delete, user holds a key down, etc). This is getting into the point of optimization where it simply does not matter and can actually harm things
Holding a key would indeed require both on key down and up. I'd still argue that handling rerender on key down (or to fully match whatever OS/browser semantics, oninput) makes more sense than key up. Pressing Ctrl+V for example produces feedback as soon as "V" is pressed, not when Ctrl and/or V is released.
Interestingly Ctrl+V on OP's website does update immediately when Ctrl+V is pressed.