Right now Ghost’s Network / ActivityPub notes are all public. There is no way to make a private mention, and… (what I have just realized is) if anyone mentions privately your Ghost account on i.e. Mastodon you will not receive anything (and the sender will not receive any message that their private mention won’t arrive to its destination).
Private mentions are important complement for network engagement. If you are using other social network as an engagement tool, how much use do you make of sent/received private messages? At least for me it has always been part of a qualitative engagement. You publish your public posts, you get some public feedback, and from time to time someone reaches out privately for more, or for something beyond the usual.
What is worse in the current situation is that whoever sends you a private response from the Fediverse will not get any hint that the message isn’t received, and they will feel legitimately ignored – which is the opposite of engagement. It just happened to me, and it was good that my personal Mastodon account was included in the same private mention – otherwise I wouldn’t have known.