Build a Calendly-style meeting booking link tool

I run a lot of calls with clients and partners, and the endless back-and-forth of "does Tuesday work, no how about Thursday" is eating my week. I want a web application that gives me a personal booking link I can drop into an email or a signature. When someone opens it, they see only my real free time, pick a slot, confirm, and the meeting appears on both our calendars without me lifting a finger. This is strictly a self-service meeting-booking tool, not a staff shift planner and not just a reminder sender.

The core of the job is availability and calendar sync done right. The tool must connect to my calendar, read existing busy events so it never double-books, and write the confirmed meeting straight back. Timezone handling has to be flawless: the person booking should see slots in their own local time while I keep mine, and the invite must carry the correct time for everyone. I also want configurable rules per meeting type, so a quick fifteen-minute intro and a full hour-long review can each have their own duration, working hours, and minimum notice.

Practical scheduling controls matter to me as much as the pretty booking page. I need buffers before and after meetings so I am never slammed with three calls in a row, daily caps so a busy day cannot overflow, and automated email confirmations plus a cancel-or-reschedule link for the guest. Please share examples of similar scheduling or calendar work you have built.

— Personal booking link with multiple meeting types, each with its own duration and rules
— Two-way calendar sync that reads busy time and writes confirmed events
— Automatic timezone detection so guests book in their local time
— Buffers before and after, minimum notice, and daily meeting caps
— Automated confirmation emails plus self-service cancel and reschedule