there's many conversations and profiles I want to sort "bookmark" for later and not engage "right now".

Please add this option on the user profiles. Then on on the messages you should be able to pick the "saved for later" and show only those profiles.

If I chose a conversation (I'd like to leave unread for now) and pick save for later, it should disappear hidden out of the main inbox... perhaps unless they message you again. "hide and save for later" basically, similar to snoozing an email.

This could be easily done with implementing custom lists as well.