No effect from CloudKit container API token discoverability checkbox

An iOS app I'm developing also has an external website where users can contribute data to the app's CloudKit public database. Using CloudKit JS, I require users to log in with their Apple ID on the website before submitting data that is sent to the public database. I need to capture the user's name and/or email address from their Apple ID info so the contributed data can be tied to a particular person, I can limit how much data each person contributes, etc. It all works great if I log in with my Apple ID, including that the web app captures my name and saves it to the public database.

The problem is that for any other Apple ID I try (a family member's or friend's, or a sandbox one I've created), the web app cannot obtain the user's name or email address, even when they successfully authenticate with their Apple ID. I also can't figure out how to make the web app ask the user for permission for their name or email to be discoverable. On the CloudKit container page where I created the web API token, I checked the box for "Request user discoverability at sign in", but that doesn't make any prompt appear during the login process. Anyone know how to force a prompt to the user to let their info be discoverable?

Thanks!