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OAuth only makes sense if they provide an API for iCloud calendar, which isn't the case as far as I know.

It's a bog-standard CalDAV server, which isn't an API, of course, but at the same time, it sorta is.

I'd argue that CalDAV is an API - it's specified and offers operations on data. It's not JSON-Rest but an API it is.

CalDAV most certainly is an API. It's standardized [1] and everything.