The rumored "Private" status feature has been officially implemented in today's updated Steam Beta Client. Now, players can set their gameplay status to "private", preventing notifications that reveal their gameplay status for specific games. This update is currently in the beta version and has not been rolled out to the official release, but players can test this feature by going to Steam Settings > Interface > setting the "Client Beta Participation" option to "Steam Beta Update".
Besides being able to turn on the "private" status for games already owned, the latest update also includes Inline Gifting, One Cart Across All Devices, and Private Purchasing features for the shopping cart. The Private Purchasing feature allows players to set a game's status to "private" before making a purchase.