Integrating advanced booking system

I am looking for a way to build out a type of booking system like on the linked website

I need to connect instructors to each course, and ideally let them (through a profile?) register when they are available. I know I can build a CMS for instructors, and for golf courses, and connect them there, but I do not know how to connect this to a booking system and calendar of avaliability.
I then need to have the booking system as shown in the link (not my site), that get populated for each golf course depending on if there are instructors available.
Customers should then be able to see the available time slots, and make an appointment.

One not is that this system does not actually book a course at the given golf course, but it lets us know that this is where the customer wants to be.

Is there any good integrations to build this out with, or examples of webflow websites that uses a similar system to this?