A good example of this is Nextcloud. The SW is FOSS. Over 400K installations are hosted in many ways including on home single board computer servers, Synology NAS, on a VPS, or as a service from providers such as https://ppp.woelkli.com/ or Hetzner.com. The calendar app is very functional and allows booking of appointments based on availability similar to Calendly. This is one of many apps within its large and expanding suite.

Another noteworthy one is Talk: https://nextcloud.com/talk/

It's not quite as good as something like a self-hosted instance of Mattermost or even Rocket.Chat, but honestly if you already have Nextcloud, then it's pretty cool to be able to get something decent like that up and running quickly.

Ofc that's making Nextcloud a single point of failure in some ways and occasionally things can go sideways with these plugin based platforms (historically applies more to installs of Jenkins, but also have had some performance issues with Nextcloud that had lots of apps, too).

I still rather like Nextcloud because of being able to just run it on my servers and replace a bunch of other third party cloud platforms and still somehow manage to have good enough uptime and security.

I wonder what other cool self-hosted platforms are out there, maybe some of what Odoo has (cool idea but a bit underwhelming last I checked): https://github.com/odoo/odoo and https://www.odoo.com/

Or something in: https://github.com/awesome-selfhosted/awesome-selfhosted