The way you move your mouse, the timing of the click button down/button up events, all those things go into some algo to determine if you're a bot or not
No, not at all. The click is not important / needed, what matters is that by moving the mouse you're granting Cloudflare's JS permission to execute functions in the background that can't run without user interaction.
The article stated that this has nothing to do with it and the click would technically not even be necessary. It is just a way to start the procedure where Turnstile verifies your browser.
Well, so much for my reading comprehension skills...