Hi, Marin. I've had this implemented using other tools where I had two collections on a schedule control: one with appointments and one with (in my own project terms) "time slots" which only had start date time, duration and CSS class to render, and were rendered on background. Appointments had a little padding, so background would also be visible.
So it could either be two different source data collection, or an appointment may have a flag that turns it into a"timeslot" that gets rendered as a background.
Hope, it helps.