How to integrate appointment setting with Calendly with your App?

Calendly integration lets your app or website connect to Calendly so people can book meetings without back-and-forth emails. You show available times from your calendar, the user picks a slot, and Calendly automatically sends invites, reminders, and updates your calendar. You can also capture extra info (like agenda or phone number) and trigger actions in your app when a meeting is scheduled or canceled.

Example: On a sales page, a “Book a demo” button opens Calendly, the prospect selects Tuesday 3:00 PM, and your CRM is updated while both sides get calendar invites and reminder emails.

Integrate Calendly bookings into my app.

Requirements:
– Backend: fetch bookings via Calendly API.
– Frontend: dashboard widget showing upcoming events (title, time, attendee).
– Supabase table `bookings (id, user_id, event_name, date, attendee_email)`.
– Auto-sync new bookings every hour (edge cron).
– Output: working booking sync + dashboard component.