"Not Available" "Error Description not available" when getting recovery code for a friend

I have a family member who added me as a recovery contact. When I try to get the Recovery Code for them, on my iPad, iPhone or MacBook Air, I get the following message:

Not Available

Error Description not available.

I, and he, meet all the requirements listed on the What Is Account Recovery and How to use account recovery when... pages. So reposting those links won't help.

We have been on the phone with Apple support and they can't even see to find documentation on what this error is. I only see one post here on it that has the unhelpful above mentioned pages. Has anyone else run into this and found a solution or gotten one from Apple?

He is on my family account. As far as I know his account is not in account recovery mode. His email address on the Recovery Contacts entry does match what shows in the Family list for iCloud.

My iPhone, iPad and MacBook are completely up to date with the latest OS versions. At this point, I don't have any clue what might be going on. We have gotten disconnected from Apple while waiting for the agent to investigate the issue. I'm not sure whether it's a good or alarming sign that on al of the internet, there is only one discussion post about this, which has a non-useful pat answer reply, and was then closed.