When a direct message, a message request, a group or Magpie support has a message you have not read, a red dot shows on your avatar in the page bar. On a phone it shows on the menu button. The account menu lists Unread messages with the number of conversations, and opens the latest one. Team channels do not add the dot.
Magpie staff can now start a direct message with anyone. It opens as an ordinary conversation, not a request, whatever Who can message you is set to. Blocking a staff member still stops them messaging you. Everyone else follows the setting as before.