https://www.addevent.com/products/calendarx

I realize this isn’t a perfect match for your requirements but my company has used various products from AddEvent over the years and they’ve always been a great experience for our end users (primarily their URL based add event to calendar functionality). It looks like they offer an embedded calendar solution potentially with the scheduling functionality you’re looking for.

Hope this helps!

I'm not aware of any full fledged solution. I built my own in the same stack, DM for more, email is in profile

fullcalendar.io