We’re using an MDM (applemdm.com) but I’ve also tried setting it up manually on the macOS machines. Also, I’ve just compared the profile settings generated by mailcow - which are the same as the one our MDM pushes.
iOS works fine for me, too. I’m only having these issues on macOS. And there it seems to be related to Ventura. On Monterey, things worked fine. After upgrading to Ventura, things still worked fine until I had to re-push the MDM profile (which caused the accounts to be recreated on the macOS machines). After that (or manually setting up the accounts), the primary calendar is no longer synced.
I’m really curious where the issue lies. I’ve also got a NextCloud instance running and using the calendar feature there as well - and there I have no issues with the primary calendar. So it doesn’t seem to be an issue with macOS primarily. Or at least not generally with CalDAV on macOS, but rather some kind of edge case.