Calls between attorneys negotiating a settlement aren't privileged. The "confidentiality" of settlement negotiations isn't confidentiality in the normal sense; rather, it simply establishes that you can't take material from settlement discussions and introduce it as evidence in a subsequent civil trial: it frees the parties to discuss things without having to worry about answering for every word they say in a subsequent trial.

If you've ever been involved in a civil conflict, you've noticed: every single piece of paper exchanged is marked "confidential settlement communication". You can publish all of it if you want.

You don't have to take my word for it (though: I've been in civil disputes, noticed this, and asked about it); legal experts on Twitter were dunking on pundits for thinking these conversations were confidential in the normal sense.