If you had done this on a Mac, it would have worked just fine. The failure in your chain is iOS Calendar not being an intent handler for ICS files.

Another way you could have solved it would be to have the Google Workspace connection set up in the backend for Claude and it would write the parsed events to your account directly. Then in iOS you could move the events to the iCloud Family Calendar.

Or again, if you did this on a Real Computer, you could bulk-move them.