> Proper ZK proofs don’t work that way. N different proofs will not be linked to each other

in theory. How do you do that on paper? How do you "anonymize" this data, to make it so they aren't related to each other?

This is just like Facebook implementing the Signal protocol on WhatsApp. They technically can't access your messages, but they have all the metadata which most of the times will allow someone to infer the content of the conversation.