Does ActivityPub even support interactions that are actually private? Last time I worked with it, the private messaging was more akin to "please don't read this postcard" in the mailbox.
I guess it depends on your definition of privacy but if you're thinking about end-to-end encryption then there's nothing like that in ActivityPub. Admins of the receiver and the sender can see all messages including direct messages. They are not visible to the broader public though.