I think the confusion is that this isn’t a CalDAV concern. A CalDAV server only hosts event/task definitions. It doesn’t do anything with them, only offers an API for managing them.

It’s the client apps that use those definitions to work out occurances, do notifications, send emails etc.

So what you want is a capable calendar app with CalDAV support and email support, that can send email invites using different email addresses for different calendars.