How can I solve "Cannot Start Family Sharing" error, when trying to set up family sharing?
Oh.

Okay, I found a hint in an email from 2012 (!) when MobileMe transitioned into iCloud (remember that!?), and I guess I had another account back then which for reasons unknown I apparently family shared to my new account ‍♂️

My strange past behaviour aside this looks to resolve my issue (waiting for account deletion to go through before I can know for sure).

If anyone else comes across this: https://appleid.apple.com guided me towards my long-lost account, and https://privacy.apple.com is where I put it up for deletion.