Booking for hotel

I need help adding a third-party booking system on my web-flow website I am using this for an inn and I want to add a booking system that when I book something it will appear on my third-party booking system or room as booked, please inform me if you know how?

Currently, i am using little hotelier but am going to switch so any suggestions on what to use as well

Here is my site Read-Only: LINK
(how to share your site Read-Only link)