"Mute" Notifications for individual conversations
Separate from the global notification settings for the application itself (which are managed by Settings) would be the per-conversation settings, i.e. one should be able to "mute" incoming notifications for individual conversations which would mean suppressing on-screen popup notifications and sounds for that conversation.
Toggling this would-be option in the conversation popover would disable all notifications for that conversation, however in the conversation list we would still see the messages badge and count (as we still need to show that there are messages incoming) but it would be greyed out to indicate the conversation mute status, opposed to the usual blue.