Closest thing today: Calendar by Form* (calendar.formstr.app, code at github.com/formstr-hq/nostr-calendar, latest release v2.4.0 on Sept 15).
What it does: NIP-52 calendar events, private events encrypted with NIP-59 gift wrap (relays can't read them), recurring events, invites by npub, .ics export, and sign-in with NIP-07, NIP-46 bunkers or Amber.
The CalDAV part is the gap. The Form* team said in June they don't expose events over CalDAV and have no near-term plan, because the server would need your nsec to decrypt private events. Their Android app can read your device calendars, so DAVx5 pulling a CalDAV server into Android plus Form* gives one combined view, read-only.
One-way out for public events: eventindex.space reads NIP-52 events from your key and serves them as an iCalendar feed you can subscribe to. There's also an open (stale) cal.com PR adding a NIP-52 calendar integration, calcom PR 24266.
