The booking links open Google's appointment scheduler in a dialog on the page. Until you open it, nothing is loaded from Google and Google learns nothing about your visit.
Once open, the scheduler is Google's own page running inside ours. Google receives your IP address, browser information and whatever you enter into it, and may set its own cookies, depending on your browser's settings. That processing is governed by Google's privacy policy, not this one.
A booking you complete there arrives in our calendar, which is where we then hold your name, email address and any message you added.