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/paths.rs

@@ -66,3 +66,25 @@ pub fn hyperhive_socket() -> PathBuf {
     std::env::var_os("HIVE_CONTROL_SOCKET")
         .map_or_else(|| PathBuf::from("/run/hive/mcp.sock"), PathBuf::from)
 }
+
+/// Directory where MCP daemons write loose-end summary files for the harness.
+/// Each daemon writes `<name>.json` here; the harness scans the dir in
+/// `get_loose_ends` to surface active work from all MCPs generically.
+///
+/// NOTE: the base-dir resolution logic here is intentionally mirrored in
+/// `hive-ag3nt/src/mcp_loose_ends.rs::loose_ends_dir()`. They can't share
+/// code across crates — keep them in sync if the fallback logic changes.
+#[must_use]
+pub fn mcp_loose_ends_dir() -> PathBuf {
+    let base = if let Some(p) = std::env::var_os("HYPERHIVE_HARNESS_DIR") {
+        PathBuf::from(p)
+    } else {
+        let state = std::env::var("HYPERHIVE_STATE_DIR").unwrap_or_default();
+        let state_path = PathBuf::from(&state);
+        state_path
+            .parent()
+            .map(|p| p.join("harness"))
+            .unwrap_or_else(|| PathBuf::from(state))
+    };
+    base.join("mcp-loose-ends")
+}