feat: surface pending matrix invites in get_loose_ends

Write mcp-loose-ends/matrix.json on invite arrival (before wake) and
after join_room clears an invite. The harness scans mcp-loose-ends/
generically in get_loose_ends, so pending invites are visible there
without any harness-side changes.

- paths: add mcp_loose_ends_dir() (mirrors hive-bash-mcp pattern)
- handlers: add refresh_invite_loose_ends() — atomic tmp+rename write
- handlers: join_room calls refresh after successful join to clear entry
- timeline: install_invite_handler refreshes loose-ends before wake

hive-matrix-mcp/src/timeline.rs

@@ -91,7 +91,7 @@ pub fn install_invite_handler(client: &Client, hyperhive_socket: PathBuf) {
     let socket = Arc::new(hyperhive_socket);
     let own_user = client.user_id().map(std::borrow::ToOwned::to_owned);
     client.add_event_handler({
-        move |event: StrippedRoomMemberEvent, room: Room, _client: Client| {
+        move |event: StrippedRoomMemberEvent, room: Room, client: Client| {
             let socket = socket.clone();
             let own_user = own_user.clone();
             async move {
@@ -108,6 +108,9 @@ pub fn install_invite_handler(client: &Client, hyperhive_socket: PathBuf) {
                 let room_id = room.room_id().to_owned();
                 let label = room.name().unwrap_or_else(|| room_id.to_string());
                 tracing::info!(%room_id, "matrix: received room invite, waking agent");
+                // Refresh loose-ends BEFORE waking so the invite is
+                // visible in get_loose_ends during the agent's turn.
+                handlers::refresh_invite_loose_ends(&client).await;
                 let body = format!(
                     "[matrix] invited to {label} ({room_id}) — \
                      use list_invites to see pending invites, join_room to accept"