Good questions, Sarang. Personally, I think your requirements raise more questions. First of all, you've already mentioned that Calendly won't work for you, so I'll not dive further into Calendly for you.

Calendso has rebranded to cal.com and I'm looking into what that service does exactly.

I have a longer list of tools at https://yoursales.com/sales-stack-2021#scheduling with more detailed comparison at https://tech.yoursales.com/scheduling .

Your requirements: Ability to create a calendar for every user in my system: most calendar tools should be able to do that.

Allow everyone to set their availability and Off Days. They should also be able to change the availability for a specific day: This seems quite possible as well with most calendar systems.

Ability for the system to book a timeslot on any of the user's calendars: You mean, in random fashion, like round-robin or as the person scheduling decides???

Ability to check conflicts before booking a slot:: This seems quite possible as well.

Ability to get notified via Webhooks whenever someone cancels the already booked slots: This seems quite possible as well.

For your setup you need a few components. At minimum you need a calendar and a scheduler. Typically those to are separate.

Calendaring would be done by Google Calendar, some sort of Microsoft product, or a CalDav compatible calendar system.

The scheduling system is separate and connects to either of the calendaring systems mentioned above. The tools you mentioned in your original post are scheduling systems, which leaves another question: which calendar system would you like to use?