feat(#1134): add unread matrix messages as a loose end

When the local matrix daemon has rooms with unread notifications,
get_loose_ends now prepends an UnreadMatrix entry to the output so
agents see pending matrix activity alongside questions/reminders
without message content being exposed.

Changes:
- hive-sh4re: add LooseEnd::UnreadMatrix { rooms: u32 } variant
- hive-matrix-mcp: add DaemonRequest::UnreadCount and handler that
  counts joined rooms with notification_count > 0 (server-side push
  notification counts, cached by matrix-sdk)
- hive-ag3nt/mcp: inject UnreadMatrix entry on self-queries by
  connecting to /run/hive-matrix/socket (HIVE_MATRIX_SOCKET override);
  best-effort — agents without matrix configured are unaffected

hive-matrix-mcp/src/handlers.rs

@@ -343,3 +343,17 @@ pub async fn read_room(client: &Client, room_ref: &str, limit: Option<usize>) ->
         .collect();
     DaemonResponse::ok(&events)
 }
+
+/// Return the number of joined rooms with at least one unread
+/// notification according to the server-side push notification counts
+/// cached by the matrix-sdk client. Used by the harness to surface
+/// unread matrix activity in `get_loose_ends` without exposing
+/// message content.
+pub fn unread_count(client: &Client) -> DaemonResponse {
+    let rooms = client
+        .joined_rooms()
+        .into_iter()
+        .filter(|r| r.unread_notification_counts().notification_count > 0)
+        .count() as u32;
+    DaemonResponse::ok(&serde_json::json!({ "rooms": rooms }))
+}

hive-matrix-mcp/src/protocol.rs

@@ -81,6 +81,12 @@ pub enum DaemonRequest {
     #[serde(rename = "join_room")]
     JoinRoom { room: String },
 
+    /// Return the count of rooms with unread notifications. Used by
+    /// the harness `get_loose_ends` to surface unread matrix activity
+    /// without exposing message content.
+    #[serde(rename = "unread_count")]
+    UnreadCount,
+
     /// Liveness probe — fast "are you up?" round-trip that doesn't
     /// touch matrix-sdk. Not used by the in-tree stdio MCP bridge
     /// (which surfaces a daemon-down condition as a normal tool-call

hive-matrix-mcp/src/socket.rs

@@ -83,5 +83,6 @@ async fn dispatch(req: DaemonRequest, client: &Client) -> DaemonResponse {
         DaemonRequest::JoinRoom { room } => handlers::join_room(client, &room).await,
         DaemonRequest::ListRoomMembers { room } => handlers::list_room_members(client, &room).await,
         DaemonRequest::ReadRoom { room, limit } => handlers::read_room(client, &room, limit).await,
+        DaemonRequest::UnreadCount => handlers::unread_count(client),
     }
 }