Not sure I agree.

We expect heads of state to be able to have “private” discussions while knowing the other heads of state they may be communicating with. I can have “private” conversations with my partner, even though people know who that is.

You can also choose to anonymously communicate with no privacy, Reddit or 4chan style...

They may not be totally orthogonal, but I don’t think either privacy nor anonymity are encapsulated by each other.

You're just describing levels of privacy. Head's of state can of course have private discussions, where only the contents of conversation is private - but the fact the conversations took place are not private. Compare that to AnonA talked to AnonB - We're still aware two people communicated, but it's even more private as we can't infer their relationship (And probabilities about what might have been discussed - from other metadata of the conversation time,place,duration,frequency). And finally, perfect privacy nobody knows that a conversation took place in the first place and the contents are unknown too.

There is also still privacy in public communications when done anonymously, as you can't tie the information disclosed to the real identity (necessarily). -- Hence why for privacy purposes advertising data is often anonymized. (But again, less private of course, if ie I said I was a 2 fingered man in Poland and there is only 5 people fitting that description)

So I'd still say, perfect privacy cannot occur without anonymity.