chore(gossip): log the game field in peer_state_for_log

Add the new PeerState.game field to the presence log formatter so
gossip Announces show whether a peer is broadcasting a game. The line
previously printed name/muted/addr_id/addrs/sharing only, making the
game-presence broadcast invisible in logs (verified solely via UI
during the 2026-06-22 2-machine field test). Log-only: no wire,
protocol, or GOSSIP_PROTO change. Adds the first unit test for the
formatter (Some and None cases).

Implemented by Codex (gpt-5.5) on branch codex-log-game-field; reviewed
and gates re-run by the senior (397 lib tests, clippy --all-targets,
release build all green).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/network/gossip.rs

@@ -133,12 +133,13 @@ fn admit_state_mutation(
 
 fn peer_state_for_log(state: &PeerState) -> String {
     format!(
-        "name={:?}, muted={}, addr_id={}, addrs={}, sharing={}",
+        "name={:?}, muted={}, addr_id={}, addrs={}, sharing={}, game={:?}",
         state.name,
         state.is_muted,
         crate::short_id(&state.addr.id.to_string()),
         state.addr.addrs.len(),
-        state.sharing.is_some()
+        state.sharing.is_some(),
+        state.game
     )
 }
 
@@ -717,6 +718,16 @@ mod tests {
         EndpointAddr::from(id)
     }
 
+    #[test]
+    fn peer_state_log_includes_game() {
+        let mut state = sample_peer_state_for(fresh_id());
+        state.game = Some("Half-Life 2".to_string());
+        assert!(peer_state_for_log(&state).contains("game=Some(\"Half-Life 2\")"));
+
+        state.game = None;
+        assert!(peer_state_for_log(&state).contains("game=None"));
+    }
+
     #[test]
     fn bootstrap_client_dials_host() {
         // A non-host (client) with no retained peers dials just the ticket host.