Any CalDAV server will do. All events are synced across all properly configured devices. No need for emailing individual events. Radicale is an exception. I also find it too simple/barebones.
I have been running Baïkal for years. Multiple users and devices (iOS, Android, MacOS, Linux, Windows etc) with multiple calendars per user, a decent admin web ui, pretty lightweight, easy to install and configure and zero maintenance.
Or just set up your own exchange server.
Personally I miss a calendar frontend that can be used directly in a web browser. Like Google calendar but with everything living on my own server.
Scheduling and event management should be done in a client if you ask me.